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1. Separable algebras
by Ford, Timothy J., 1954- author
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
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2. Nonlinear elliptic equations and nonassociative algebras
by Nadirashvili, Nikolai, 1955 and Tkachev, Vladimir, 1963- author and Vlăduț, S. G. 1954- author. (Serge G.)
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
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3. Full Text Noncommutative motives of separable algebras
by Tabuada, Gonçalo and Van den Bergh, Michel
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
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4. New examples of Frobenius extensions
by Kadison, Lars
1999, University lecture series, ISBN 0821819623, Volume 14, x, 84
Separable algebras | Frobenius algebras | Hopf algebras
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5. Full Text Information and σ-algebras
by Carlos Hervés-Beloso and Paulo Klinger Monteiro
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
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6. Full Text Maximal subalgebras of finite-dimensional algebras
by Iovanov, MC and Sistko, AH
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
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7. Full Text Entanglement-breaking channels with general outcome operator algebras
by Kuramochi, Yui
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
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8. Full Text Homomorphisms onto effectively separable algebras
by Kasymov, N Kh
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
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9. Full Text On Hopf Galois Extension of Separable Algebras
by Yu LU Shenglin ZHU
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
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10. Full Text Quadratic Mappings and Clifford Algebras
by Helmstetter, Jacques and Micali, Artibano
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
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11. Full Text Unramified division algebras do not always contain Azumaya maximal orders
by Antieau, Benjamin and Antieau, Benjamin and Williams, Ben and Williams, Ben
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
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12. Full Text Tolerance types of interval eigenvectors in max-plus algebra
by Gavalec, M and Plavka, J and Ponce, D
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
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13. Full Text Towards a theory of classification
by Elliott, George A
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
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14. Full Text Construction of exposed indecomposable positive linear maps between matrix algebras
by Ha, Kil-Chan and Kye, Seung-Hyeok
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
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15. Full Text The structure of separable Dynkin algebras
by Vallander, S S
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
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16. Full Text Algebra depth in tensor categories
by Kadison, L
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
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17. Full Text On the isomorphism problem for measures on Boolean algebras
by Borodulin-Nadzieja, Piotr and Džamonja, Mirna
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
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18. Full Text Non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras
by Crespo, Teresa and Rio, Anna and Vela, Montserrat
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
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19. Full Text Graphs and CCR Algebras
by Ilijas Farah
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
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20. Separable and Frobenius monoidal Hom-algebras
by Chen, Yuanyuan and Zhou, Xiaoyan
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
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