2017, Graduate studies in mathematics, ISBN 9781470437701, Volume 183, xxi, 637 pages

Algebraic geometry -- (Co)homology theory -- Étale and other Grothendieck topologies and (co)homologies | Commutative algebra -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- General commutative ring theory -- Ideals; multiplicative ideal theory | Separable algebras | Algebraic geometry -- Local theory -- Local structure of morphisms: Étale, flat, etc | Commutative algebra -- Ring extensions and related topics -- Galois theory | Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | Commutative algebra -- Ring extensions and related topics -- Étale and flat extensions; Henselization; Artin approximation | Associative rings | Associative rings and algebras -- Instructional exposition (textbooks, tutorial papers, etc.) | Commutative algebra -- Theory of modules and ideals -- Class groups

Book

2014, Mathematical surveys and monographs, ISBN 9781470417109, Volume 200, vii, 240

Differential equations, Elliptic | Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan algebras (algebras, triples and pairs) | Nonassociative rings and algebras -- General nonassociative rings -- Division algebras | Differential geometry -- Global differential geometry -- Calibrations and calibrated geometries | Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations | Associative rings and algebras -- Algebras and orders -- Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) | Calculus of variations and optimal control; optimization -- Manifolds -- Minimal surfaces | Jordan algebras | Nonassociative rings

Book

Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 1122 - 1161

In this article we study in detail the category of noncommutative motives of separable algebras over a base field . We start by constructing four different...

Separable algebra | dg Azumaya algebra | Hecke algebra | Convolution | Noncommutative motives | Brauer group | Cyclic sieving phenomenon | Twisted flag variety | VARIETIES | CATEGORIES | ADDITIVE INVARIANTS | EQUIVALENCE | AZUMAYA ALGEBRAS | MATHEMATICS | NUMERICAL MOTIVES | Aluminum compounds | Usage | Algebra | Analysis

Separable algebra | dg Azumaya algebra | Hecke algebra | Convolution | Noncommutative motives | Brauer group | Cyclic sieving phenomenon | Twisted flag variety | VARIETIES | CATEGORIES | ADDITIVE INVARIANTS | EQUIVALENCE | AZUMAYA ALGEBRAS | MATHEMATICS | NUMERICAL MOTIVES | Aluminum compounds | Usage | Algebra | Analysis

Journal Article

1999, University lecture series, ISBN 0821819623, Volume 14, x, 84

Book

Economic Theory, ISSN 0938-2259, 10/2013, Volume 54, Issue 2, pp. 405 - 418

In this work, we clarify the relationship between the information that an agent receives from a signal, from an experiment or from his own ability to determine...

Equivalence relation | Measurability | Measure theory | Urelements | Atoms | Separable spaces | Mathematics | State of nature | Probabilities | Property partitioning | Information models | Partitions | σ-algebras | Signals

Equivalence relation | Measurability | Measure theory | Urelements | Atoms | Separable spaces | Mathematics | State of nature | Probabilities | Property partitioning | Information models | Partitions | σ-algebras | Signals

Journal Article

FORUM MATHEMATICUM, ISSN 0933-7741, 09/2019, Volume 31, Issue 5, pp. 1283 - 1304

We study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field.. and obtain full classification/description...

MATHEMATICS | separable | MATHEMATICS, APPLIED | semisimple algebra | split | separable functor | split-by-nilpotent | Maximal subalgebra | COMMUTING VARIETIES | IRREDUCIBILITY | CLUSTER-TILTED ALGEBRAS

MATHEMATICS | separable | MATHEMATICS, APPLIED | semisimple algebra | split | separable functor | split-by-nilpotent | Maximal subalgebra | COMMUTING VARIETIES | IRREDUCIBILITY | CLUSTER-TILTED ALGEBRAS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 10/2018, Volume 59, Issue 10, p. 102206

A unit-preserving and completely positive linear map, or a channel, Λ:A→Ain between C*-algebras A and Ain is called entanglement-breaking (EB) if ω◦(Λ⊗idB) is...

SEPARABLE STATES | POSITIVE MAPS | PHYSICS, MATHEMATICAL | QUANTUM

SEPARABLE STATES | POSITIVE MAPS | PHYSICS, MATHEMATICAL | QUANTUM

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 1/2016, Volume 57, Issue 1, pp. 36 - 50

We study variations of the concept of separable enumeration and, basing on that, describe a series of algorithmic and algebraic concepts. In this framework we...

Artinian congruence lattice | negative and positive equivalences | Mathematics, general | Mathematics | separable and effectively separable enumerations of algebras | separability axioms | Negative and positive equivalences | Separability axioms | Separable and effectively separable enumerations of algebras | MATHEMATICS | Algebra

Artinian congruence lattice | negative and positive equivalences | Mathematics, general | Mathematics | separable and effectively separable enumerations of algebras | separability axioms | Negative and positive equivalences | Separability axioms | Separable and effectively separable enumerations of algebras | MATHEMATICS | Algebra

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2017, Volume 38, Issue 4, pp. 999 - 1018

In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left...

可分代数 | 伽罗瓦理论 | 代数域 | H-模代数 | Galois扩张 | 理想子代数 | 一一对应 | Hopf | Separable algebra | 17B40 | Galois connection | Semisimple Hopf algebra | Mathematics, general | Mathematics | Applications of Mathematics | 17B50 | Hopf Galois extension | MATHEMATICS | SEMISIMPLE EXTENSIONS | FREENESS | RINGS | Algebra

可分代数 | 伽罗瓦理论 | 代数域 | H-模代数 | Galois扩张 | 理想子代数 | 一一对应 | Hopf | Separable algebra | 17B40 | Galois connection | Semisimple Hopf algebra | Mathematics, general | Mathematics | Applications of Mathematics | 17B50 | Hopf Galois extension | MATHEMATICS | SEMISIMPLE EXTENSIONS | FREENESS | RINGS | Algebra

Journal Article

2008, 1. Aufl., ISBN 3764386053, 514

After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve...

Mathematics | Clifford algebras | Forms, Quadratic | Algebra

Mathematics | Clifford algebras | Forms, Quadratic | Algebra

eBook

Inventiones mathematicae, ISSN 0020-9910, 7/2014, Volume 197, Issue 1, pp. 47 - 56

We show that, in general, over a regular integral noetherian affine scheme X of dimension at least 6, there exist Brauer classes on X for which the associated...

Mathematics, general | Mathematics | CENTRAL SEPARABLE ALGEBRAS | MATHEMATICS | PROJECTIVE MODULES | Algebra | Integrals | Classification | Group theory | Proving | Division | Topology

Mathematics, general | Mathematics | CENTRAL SEPARABLE ALGEBRAS | MATHEMATICS | PROJECTIVE MODULES | Algebra | Integrals | Classification | Group theory | Proving | Division | Topology

Journal Article

Information Sciences, ISSN 0020-0255, 11/2016, Volume 367-368, pp. 14 - 27

Max-plus algebra plays a key role in the study of discrete event systems in connection with optimization problems such as scheduling or project management in...

Interval matrix | System dynamics | Tolerable eigenvector | Steady state | Max-plus algebra | ROBUSTNESS | MATRICES | SOLVABILITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | SEPARABLE LINEAR-EQUATIONS | SYSTEMS | Electrical engineering | Algebra | Algorithms | Functions (mathematics) | Intervals | Mathematical analysis | Eigenvectors | Polynomials | Tolerances

Interval matrix | System dynamics | Tolerable eigenvector | Steady state | Max-plus algebra | ROBUSTNESS | MATRICES | SOLVABILITY | COMPUTER SCIENCE, INFORMATION SYSTEMS | SEPARABLE LINEAR-EQUATIONS | SYSTEMS | Electrical engineering | Algebra | Algorithms | Functions (mathematics) | Intervals | Mathematical analysis | Eigenvectors | Polynomials | Tolerances

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2010, Volume 223, Issue 1, pp. 30 - 48

The well-known difficulties arising in a classification which is not set-theoretically trivial—involving what is sometimes called a non-smooth quotient—have...

Classifying category | Operator algebras | Countable groups | Countably generated Hilbert [formula omitted]-modules | Amenable [formula omitted]-algebras | Separable [formula omitted]-algebras | Classification | Classification functor | Amenable von Neumann algebras | Von Neumann algebras with separable predual | Countably generated Hilbert C | Amenable C | algebras | Separable C | modules | INDUCTIVE LIMITS | NUCLEAR | Amenable C-algebras | C-ASTERISK-ALGEBRAS | INVARIANT | Countably generated Hilbert C-modules | Separable C-algebras | MATHEMATICS | REAL RANK ZERO

Classifying category | Operator algebras | Countable groups | Countably generated Hilbert [formula omitted]-modules | Amenable [formula omitted]-algebras | Separable [formula omitted]-algebras | Classification | Classification functor | Amenable von Neumann algebras | Von Neumann algebras with separable predual | Countably generated Hilbert C | Amenable C | algebras | Separable C | modules | INDUCTIVE LIMITS | NUCLEAR | Amenable C-algebras | C-ASTERISK-ALGEBRAS | INVARIANT | Countably generated Hilbert C-modules | Separable C-algebras | MATHEMATICS | REAL RANK ZERO

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 11/2016, Volume 64, Issue 11, pp. 2188 - 2198

We construct a large class of indecomposable positive linear maps from the matrix algebra into the matrix algebra, which generate exposed extreme rays of the...

bi-spanning property | boundary | 15A30 | exposed indecomposable positive maps | 81P15 | separable states | 46L05 | full ranks | MATHEMATICS | SEPARABILITY CRITERION | STATES | Algebra | Matrix algebra | Mathematical analysis | Images | Exposure | Convexity | Hulls (structures) | Boundaries | Combinatorial analysis

bi-spanning property | boundary | 15A30 | exposed indecomposable positive maps | 81P15 | separable states | 46L05 | full ranks | MATHEMATICS | SEPARABILITY CRITERION | STATES | Algebra | Matrix algebra | Mathematical analysis | Images | Exposure | Convexity | Hulls (structures) | Boundaries | Combinatorial analysis

Journal Article

Vestnik St. Petersburg University: Mathematics, ISSN 1063-4541, 7/2016, Volume 49, Issue 3, pp. 219 - 223

Abstract Dynkin algebras are studied. Such algebras form a useful instrument for discussing probabilities in a rather natural context. Abstractness means the...

Boolean operation | Mathematics | abstract Dynkin algebra | separable Dynkin algebra | Analysis | Algebra

Boolean operation | Mathematics | abstract Dynkin algebra | separable Dynkin algebra | Analysis | Algebra

Journal Article

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 2016, Volume 23, Issue 5, pp. 721 - 752

Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple...

Frobenius extension | HOPF-ALGEBRAS | SEPARABLE EXTENSIONS | THEOREM | RINGS | SUBGROUPS | semisimple extension | core Hopf ideals | SUBALGEBRAS | tensor category | MATHEMATICS | MODULES | Morita equivalent ring extensions | relative Maschke theorem | subgroup depth | Categories (Mathematics) | Algebra | Research | Mathematical research

Frobenius extension | HOPF-ALGEBRAS | SEPARABLE EXTENSIONS | THEOREM | RINGS | SUBGROUPS | semisimple extension | core Hopf ideals | SUBALGEBRAS | tensor category | MATHEMATICS | MODULES | Morita equivalent ring extensions | relative Maschke theorem | subgroup depth | Categories (Mathematics) | Algebra | Research | Mathematical research

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2013, Volume 405, Issue 1, pp. 37 - 51

The paper investigates possible generalizations of Maharam’s theorem to a classification of Boolean algebras that support a finitely additive measure. We prove...

Maharam theorem | Uniformly regular measures | Separable measures | Boolean algebras | Borel equivalence relations | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | PROBABILITY-MEASURES | Heterocyclic compounds | Algebra

Maharam theorem | Uniformly regular measures | Separable measures | Boolean algebras | Borel equivalence relations | TOPOLOGY | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | PROBABILITY-MEASURES | Heterocyclic compounds | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2015, Volume 422, pp. 270 - 276

We give a degree 8 non-normal separable extension having two non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras.

Separable field extension | Hopf Galois structure | Hopf algebra | Galois theory | Hopf galois structure | MATHEMATICS | SEPARABLE FIELD-EXTENSIONS | Algebra | Teoria de cossos i polinomis | Field theory (Physics) | Àlgebra | Matemàtiques i estadística | Teoria de camps (física) | Àrees temàtiques de la UPC | 12F Field extensions

Separable field extension | Hopf Galois structure | Hopf algebra | Galois theory | Hopf galois structure | MATHEMATICS | SEPARABLE FIELD-EXTENSIONS | Algebra | Teoria de cossos i polinomis | Field theory (Physics) | Àlgebra | Matemàtiques i estadística | Teoria de camps (física) | Àrees temàtiques de la UPC | 12F Field extensions

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2010, Volume 59, Issue 3, pp. 1041 - 1056

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a...

Universal algebra | Mathematical set theory | Algebra | Mathematical theorems | Subalgebras | Separable spaces | Hilbert spaces | Mathematics | Mathematical relations | Vertices | Canonical commutation relations | Graphs | Representations | Simple nuclear C-algebras | MATHEMATICS | graphs | PURE STATE-SPACE | HOMOGENEITY | canonical commutation relations | C-ASTERISK-ALGEBRAS | simple nuclear C-algebras | representations

Universal algebra | Mathematical set theory | Algebra | Mathematical theorems | Subalgebras | Separable spaces | Hilbert spaces | Mathematics | Mathematical relations | Vertices | Canonical commutation relations | Graphs | Representations | Simple nuclear C-algebras | MATHEMATICS | graphs | PURE STATE-SPACE | HOMOGENEITY | canonical commutation relations | C-ASTERISK-ALGEBRAS | simple nuclear C-algebras | representations

Journal Article

Colloquium Mathematicum, ISSN 0010-1354, 2014, Volume 137, Issue 2, pp. 229 - 251

As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the...

Monoidal hom-hopf algebra | Hom-Frobenius-separability equation | Nakayama automorphism | Separable (Frobenius) monoidal hom-algebra | monoidal Hom-Hopf algebra | YANG-BAXTER EQUATION | HOPF-ALGEBRAS | separable (Frobenius) monoidal Hom-algebra | COALGEBRAS | DERIVATIONS | LIE-ALGEBRAS | MATHEMATICS | CATEGORY | CONSTRUCTION | DEFORMATIONS

Monoidal hom-hopf algebra | Hom-Frobenius-separability equation | Nakayama automorphism | Separable (Frobenius) monoidal hom-algebra | monoidal Hom-Hopf algebra | YANG-BAXTER EQUATION | HOPF-ALGEBRAS | separable (Frobenius) monoidal Hom-algebra | COALGEBRAS | DERIVATIONS | LIE-ALGEBRAS | MATHEMATICS | CATEGORY | CONSTRUCTION | DEFORMATIONS

Journal Article

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