Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings....

Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of...

p-adic integers. Combinatorial commutative algebra Invariant theory Serre's multiplicity conjectures Homological conjectures Commutative ring Module (mathematics)...

geometries. Algebraic graph theory Combinatorial commutative algebra Polyhedral combinatorics Algebraic Combinatorics (journal) Journal of Algebraic Combinatorics...

Cohomology theory Combinatorial analysis Combinatorial commutative algebra a discipline viewed as the intersection between commutative algebra and combinatorics...

ring is commutative (that is, its multiplication is a commutative operation) has profound implications on its properties. Commutative algebra, the theory...

Stanley–Reisner ring construction is a basic tool within algebraic combinatorics and combinatorial commutative algebra. Its properties were investigated by Richard...

breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and...

can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at...

isomorphic to a sub-semiring of a Boolean algebra. The commutative semiring formed by the two-element Boolean algebra and defined by 1 + 1 = 1 {\displaystyle...

homological methods. Combinatorial commutative algebra Miller, Ezra; Sturmfels, Bernd (2005). Combinatorial commutative algebra. Graduate Texts in Mathematics...

mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative ring with unity. Subalgebras...

Press, 2001 [1994] Miller, Ezra; Sturmfels, Bernd (2005). Combinatorial Commutative Algebra. Graduate Texts in Mathematics. Vol. 227. New York, NY: Springer-Verlag...

Other formulations of the vertex algebra axioms include Borcherds's later work on singular commutative rings, algebras over certain operads on curves introduced...

with non-commutative elements, one can define the determinant and prove linear algebra theorems that are very similar to their commutative analogs. Examples...

integers in number theory Difference algebra Differential algebraic geometry Differential calculus over commutative algebras Differential Galois theory – Study...

von Neumann algebras. Let R {\displaystyle R} be a commutative ring and fix δ ∈ R {\displaystyle \delta \in R} . The Temperley–Lieb algebra T L n ( δ )...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

the AWM–Microsoft Research Prize in Algebra and Number Theory. Her research involves combinatorial commutative algebra, graph theory, and tropical geometry...

it is not commutative. Therefore, the quaternions,   H   , {\displaystyle \ \mathbb {H} \ ,} are a non-commutative, associative algebra over the real...

projective toric variety. Miller, Ezra; Sturmfels, Bernd (2005), Combinatorial Commutative Algebra, Graduate Texts in Mathematics, vol. 227, New York: Springer-Verlag...

Algebraic statistics is a branch of mathematical statistics that focuses on the use of algebraic, geometric, and combinatorial methods in statistics. While...

K-theory Hodge conjecture Weil conjectures Directed algebraic topology Example: DE-9IM Chain complex Commutative diagram Exact sequence Five lemma Short five...

specifically in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has...

secondary-school mathematics textbooks Melody Chan, American expert in combinatorial commutative algebra, graph theory, and tropical geometry Sun-Yung Alice Chang...

defined and described combinatorially by Ola Bratteli. Later, George A. Elliott gave a complete classification of AF algebras using the K0 functor whose...

and Green's hyperplane restriction theorem", Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects, CRC Press, ISBN 978-1-420-02832-4...

The relation of real algebra to real algebraic geometry is similar to the relation of commutative algebra to complex algebraic geometry. Related fields...

stimulated the development of the new interdisciplinary field combinatorial commutative algebra. Member of the Academy of Sciences of the Islamic Republic...

1016/0001-8708(78)90037-3. Miller, Ezra; Sturmfels, Bernd (2005). Combinatorial Commutative Algebra. Graduate Texts in Mathematics. Vol. 227. Springer. ISBN 978-0-387-23707-7...