Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2019, Volume 371, Issue 5, pp. 3549 - 3592

We show that Écalle's transseries and their variants (LE and EL-series) can be interpreted as functions from positive infinite surreal numbers to surreal...

Composition | Surreal numbers | Transseries | MATHEMATICS | FIELDS | NUMBERS | transseries | composition | Mathematics - Logic

Composition | Surreal numbers | Transseries | MATHEMATICS | FIELDS | NUMBERS | transseries | composition | Mathematics - Logic

Journal Article

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 3/2018, Volume 59, Issue 1, pp. 77 - 100

We trace derivations through Demazure’s correspondence between a finitely generated positively graded normal k-algebras A and normal projective k-varieties X...

Geometry | Euler sequence | Graded linear series | Algebra | Secondary 14C20 | Convex and Discrete Geometry | Derivation | Algebraic Geometry | Mathematics | Graded algebra | 14N05 | Primary 13N15 | Mathematics - Algebraic Geometry

Geometry | Euler sequence | Graded linear series | Algebra | Secondary 14C20 | Convex and Discrete Geometry | Derivation | Algebraic Geometry | Mathematics | Graded algebra | 14N05 | Primary 13N15 | Mathematics - Algebraic Geometry

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2015, Volume 43, Issue 5, pp. 1935 - 1938

Let R be a UFD, and let M(R, n) be the set of all subalgebras of the form R[f], where f ∈ R[x 1 ,..., x n ]∖R. For a polynomial f ∈ R[x 1 ,..., x n ]∖R, we...

Secondary: 13N15 | Derivation | Closed polynomial | Primary: 13B25 | MATHEMATICS | CONSTANTS | DERIVATIONS

Secondary: 13N15 | Derivation | Closed polynomial | Primary: 13B25 | MATHEMATICS | CONSTANTS | DERIVATIONS

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2016, Volume 44, Issue 11, pp. 4811 - 4822

The main purpose of this paper is to provide several results on objects lying between differential geometry and algebraic geometry such as C ∞ -rings and...

Secondary: 58A20 | C | ring | Differential manifold | Primary: 13N15 | Derivation | Jet | Weil algebra | ∞

Secondary: 58A20 | C | ring | Differential manifold | Primary: 13N15 | Derivation | Jet | Weil algebra | ∞

Journal Article

Communications in Algebra, ISSN 0092-7872, 03/2016, Volume 44, Issue 3, pp. 1196 - 1199

Recently, Edo and Poloni constructed a family of tame automorphisms of a polynomial ring in three variables which degenerates to a wild automorphism. In this...

Secondary: 13N15 | Degeneration | Polynomial automorphism | Tame subgroup | Primary: 14R10 | Ind-group | MATHEMATICS

Secondary: 13N15 | Degeneration | Polynomial automorphism | Tame subgroup | Primary: 14R10 | Ind-group | MATHEMATICS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 11/2017, Volume 109, Issue 5, pp. 461 - 469

The first main theorem of this paper asserts that any $$(\sigma , \tau )$$ ( σ , τ ) -derivation d, under certain conditions, either is a $$\sigma $$ σ...

Secondary 13N15 | von Neumann algebra | Derivation | Mathematics, general | Mathematics | sigma $$ σ -derivation | ( $$\sigma $$ σ , $$\tau $$ τ )-derivation | Primary 47B47 | 46L10

Secondary 13N15 | von Neumann algebra | Derivation | Mathematics, general | Mathematics | sigma $$ σ -derivation | ( $$\sigma $$ σ , $$\tau $$ τ )-derivation | Primary 47B47 | 46L10

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 06/2016, Volume 93, Issue 3, pp. 590 - 618

We prove that the theories of fields with Hasse–Schmidt derivations corresponding to actions of formal groups admit model companions. We also give geometric...

MATHEMATICS | VARIETIES | Derivation | Mathematical models | Mathematics - Logic

MATHEMATICS | VARIETIES | Derivation | Mathematical models | Mathematics - Logic

Journal Article

manuscripta mathematica, ISSN 0025-2611, 9/2019, Volume 160, Issue 1, pp. 1 - 8

We show that a holonomic divisor is free if and only if applying all logarithmic derivations to a generic function with isolated critical point yields a...

Geometry | Primary 32S65 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | 13N15 | Number Theory | Secondary 13H10 | MATHEMATICS | Algebra | Mathematics - Algebraic Geometry

Geometry | Primary 32S65 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | 13N15 | Number Theory | Secondary 13H10 | MATHEMATICS | Algebra | Mathematics - Algebraic Geometry

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 6/2018, Volume 92, Issue 3, pp. 581 - 597

We continue the study of additive functions $$f_k:R\rightarrow F \;(1\le k\le n)$$ fk:R→F(1≤k≤n) linked by an equation of the form $$\sum _{k=1}^n...

Functional equation | Mathematics | Integral domain | Characteristic zero | Ring derivation | Higher-order derivation | Secondary: 13N15 | Field | Analysis | Homogeneity | 16W25 | Combinatorics | 39B72 | Primary: 39B52

Functional equation | Mathematics | Integral domain | Characteristic zero | Ring derivation | Higher-order derivation | Secondary: 13N15 | Field | Analysis | Homogeneity | 16W25 | Combinatorics | 39B72 | Primary: 39B52

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2018, Volume 46, Issue 8, pp. 3413 - 3429

We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible aﬃne variety X is simple if...

Lie algebra of vector fields | 17B66 | Secondary: 13N15 | Primary: 17B20 | smooth algebraic variety | Functions (mathematics) | Algebra | Mathematical analysis | Group theory | Linear algebra | Lie groups | Polynomials | Fields (mathematics) | Quantum theory

Lie algebra of vector fields | 17B66 | Secondary: 13N15 | Primary: 17B20 | smooth algebraic variety | Functions (mathematics) | Algebra | Mathematical analysis | Group theory | Linear algebra | Lie groups | Polynomials | Fields (mathematics) | Quantum theory

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2017, Volume 145, Issue 5, pp. 1865 - 1879

By an additive action on an algebraic variety X of dimension n we mean a regular action \mathbb{G}_a^n\times X\to X with an open orbit of the commutative...

Unipotent group | Automorphism | Locally nilpotent derivation | Demazure root | Cox ring | Toric variety | EQUIVARIANT COMPACTIFICATIONS | MATHEMATICS, APPLIED | locally nilpotent derivation | automorphism | HASSETT-TSCHINKEL CORRESPONDENCE | unipotent group | MATHEMATICS | BOUNDED HEIGHT | POINTS | FLAG VARIETIES | Mathematics - Algebraic Geometry

Unipotent group | Automorphism | Locally nilpotent derivation | Demazure root | Cox ring | Toric variety | EQUIVARIANT COMPACTIFICATIONS | MATHEMATICS, APPLIED | locally nilpotent derivation | automorphism | HASSETT-TSCHINKEL CORRESPONDENCE | unipotent group | MATHEMATICS | BOUNDED HEIGHT | POINTS | FLAG VARIETIES | Mathematics - Algebraic Geometry

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 2018, Volume 18, Issue 10

We provide an explicit description of homogeneous locally nilpotent derivations of the algebra of regular functions on affine trinomial hypersurfaces. As an...

torus action | Affine hypersurface | graded algebra | derivation | VARIETY | MATHEMATICS | MATHEMATICS, APPLIED | AFFINE

torus action | Affine hypersurface | graded algebra | derivation | VARIETY | MATHEMATICS | MATHEMATICS, APPLIED | AFFINE

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 1924 - 1930

Let A = k [3] be the polynomial ring in three variables over a field k, and let D be a nontrivial locally finite iterative higher derivation on A. Let A D...

Secondary: 14R10 | 13N15 | Locally finite iterative higher derivation | Primary: 13A50 | Cancellation problem | Kernels | Theorems | Algebra | Theorem proving | Mathematical analysis | Cancellation | Derivation | Rings (mathematics)

Secondary: 14R10 | 13N15 | Locally finite iterative higher derivation | Primary: 13A50 | Cancellation problem | Kernels | Theorems | Algebra | Theorem proving | Mathematical analysis | Cancellation | Derivation | Rings (mathematics)

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2017, Volume 91, Issue 2, pp. 317 - 330

This article has two aims. First, we provide the solution to a problem posed by the author in a previous paper. Second, we consider a problem posed by...

Functional equation | Mathematics | Integral domain | Characteristic zero | Ring derivation | Higher-order derivation | Field | Primary 39B52 | Secondary 13N15 | Analysis | Homogeneity | 16W25 | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Derivation | Additives | Mathematical analysis

Functional equation | Mathematics | Integral domain | Characteristic zero | Ring derivation | Higher-order derivation | Field | Primary 39B52 | Secondary 13N15 | Analysis | Homogeneity | 16W25 | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Derivation | Additives | Mathematical analysis

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2017, Volume 67, Issue 1, pp. 17 - 22

In this paper, the notion of derivation on partially ordered sets is introduced and studied. Several characterization theorems on derivations are presented....

ideal | partially ordered set | fixed point | Primary 03G10 | Derivation | 13N15 | Secondary 06D35 | MATHEMATICS | LATTICES | Fixed point theory | Research | Mathematical research | Ordered sets | Fixed points (mathematics)

ideal | partially ordered set | fixed point | Primary 03G10 | Derivation | 13N15 | Secondary 06D35 | MATHEMATICS | LATTICES | Fixed point theory | Research | Mathematical research | Ordered sets | Fixed points (mathematics)

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 4/2016, Volume 90, Issue 2, pp. 335 - 340

In this note we provide the solution to a problem posed by the first author in a previous paper. In particular, we prove a result relating the number of...

Primary 39B52 | Secondary 13N15 | functional equation | characteristic zero | Analysis | Derivation | integral domain | 16W25 | Mathematics | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Functional equations | Mathematical analysis

Primary 39B52 | Secondary 13N15 | functional equation | characteristic zero | Analysis | Derivation | integral domain | 16W25 | Mathematics | Combinatorics | 39B72 | MATHEMATICS | MATHEMATICS, APPLIED | Functional equations | Mathematical analysis

Journal Article

17.
Full Text
Applications of differential algebra to algebraic independence of arithmetic functions

Acta Arithmetica, ISSN 0065-1036, 2016, Volume 172, Issue 2, pp. 149 - 173

Acta Arith. 172. (2016) no. 2 149-173 We generalize and unify the proofs of several results on algebraic in- dependence of arithmetic functions and Dirichlet...

Algebraic and linear dependence | Differential schanuel conjecture | Arithmetic functions | Formal dirichlet series | Ax's theorem | MATHEMATICS | differential Schanuel conjecture | DIRICHLET SERIES | arithmetic functions | formal Dirichlet series | algebraic and linear dependence | Mathematics - Number Theory

Algebraic and linear dependence | Differential schanuel conjecture | Arithmetic functions | Formal dirichlet series | Ax's theorem | MATHEMATICS | differential Schanuel conjecture | DIRICHLET SERIES | arithmetic functions | formal Dirichlet series | algebraic and linear dependence | Mathematics - Number Theory

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 6/2015, Volume 89, Issue 3, pp. 685 - 718

We provide a unifying framework for the treatment of equations of the form $$\sum_{k=1}^n x^{p_k} f_k (x^{q_k}) = 0$$ ∑ k = 1 n x p k f k ( x q k ) = 0 for...

Primary 39B52 | Secondary 13N15 | Analysis | Derivation of higher order | 16W25 | Homogeneous function | Mathematics | Integral domain | Combinatorics | Additive map | 39B72 | Ring derivation | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical problems | Mathematical functions | Maps

Primary 39B52 | Secondary 13N15 | Analysis | Derivation of higher order | 16W25 | Homogeneous function | Mathematics | Integral domain | Combinatorics | Additive map | 39B72 | Ring derivation | FORMS | MATHEMATICS | MATHEMATICS, APPLIED | Mathematical problems | Mathematical functions | Maps

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2012, Volume 40, Issue 8, pp. 2841 - 2852

We discuss various sufficient conditions, involving derivations and jacobians, for elements of a domain of characteristic p > 0, to form a p-basis of a ring of...

Derivation | p-Basis | Ring of constants | Secondary 12H05, 13F15 | Primary 13N15 | POLYNOMIALS | MATHEMATICS | CONSTANTS | RINGS | K | DERIVATIONS

Derivation | p-Basis | Ring of constants | Secondary 12H05, 13F15 | Primary 13N15 | POLYNOMIALS | MATHEMATICS | CONSTANTS | RINGS | K

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 01/2013, Volume 217, Issue 1, pp. 165 - 171

Let k be a field of characteristic zero. Let φ be a k-endomorphism of the polynomial algebra k[x1,…,xn]. It is known that φ is an automorphism if and only if...

MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | DERIVATIONS | RINGS | Algebra

MATHEMATICS | MATHEMATICS, APPLIED | CONSTANTS | DERIVATIONS | RINGS | Algebra

Journal Article

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