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searching for Integral domain 21 found (252 total)

Regular extension (341 words) [view diff] exact match in snippet view article find links to article

equivalently, L ⊗ k k ¯ {\displaystyle L\otimes _{k}{\overline {k}}} is an integral domain when k ¯ {\displaystyle {\overline {k}}} is the algebraic closure of

Finitely generated module (2,837 words) [view diff] exact match in snippet view article find links to article

generated by one element, it is called a cyclic module. Let R be an integral domain with K its field of fractions. Then every finitely generated R-submodule

Schreier domain (161 words) [view diff] exact match in snippet view article find links to article

be written as x = x1 x2 so that x1 divides y and x2 divides z. An integral domain is said to be pre-Schreier if every nonzero element is primal. A GCD

Vector potential (686 words) [view diff] exact match in snippet view article find links to article

= v . {\displaystyle \nabla \times \mathbf {A} =\mathbf {v} .} The integral domain can be restricted to any simply connected region Ω {\displaystyle \mathbf

Serre's criterion for normality (956 words) [view diff] exact match in snippet view article find links to article

trivially follow from the definitions. Item 2 is much deeper. For an integral domain, the criterion is due to Krull. The general case is due to Serre. (After

Regular local ring (1,874 words) [view diff] exact match in snippet view article find links to article

but need not be an integral domain. For example, the product of two regular integral domains is regular, but not an integral domain. Geometrically regular

Mori–Nagata theorem (224 words) [view diff] exact match in snippet view article find links to article

1090/s0273-0979-1990-15896-3 Mori, Yoshiro (1953), "On the integral closure of an integral domain", Memoirs of the College of Science, University of Kyoto. Series A:

Locally nilpotent derivation (4,374 words) [view diff] exact match in snippet view article find links to article

characteristic zero, to give a locally nilpotent derivation on the integral domain A {\displaystyle A} , finitely generated over the field, is equivalent

Regular sequence (1,229 words) [view diff] exact match in snippet view article find links to article

dimension of M (also called the dimension of the support of M). Given an integral domain R {\displaystyle R} any nonzero f ∈ R {\displaystyle f\in R} gives

Yoshiro Mori (mathematician) (53 words) [view diff] exact match in snippet view article

domains.[when?] Mori, Yoshiro (1953), "On the integral closure of an integral domain", Memoirs of the College of Science, University of Kyoto. Series A:

Analytic space (1,031 words) [view diff] exact match in snippet view article find links to article

the structure sheaf is a normal ring (meaning an integrally closed integral domain). In a normal analytic space, the singular locus has codimension at

Ideal theory (1,095 words) [view diff] exact match in snippet view article find links to article

definition of a fractional ideal is not clear). However, over a Noetherian integral domain, it is still possible to develop some theory generalizing the situation

Glossary of field theory (2,063 words) [view diff] exact match in snippet view article find links to article

extension. Self-regular extension An extension E/F such that E ⊗F E is an integral domain. Totally transcendental extension An extension E/F such that F is algebraically

Kingdom of Reman (2,673 words) [view diff] exact match in snippet view article find links to article

the two separate territories (Yala and Hulu Perak) that once form an integral domain of the kingdom. The areas till today are marked by a Patani-Reman influence

Improper integral (4,172 words) [view diff] exact match in snippet view article find links to article

a value in this way, as the integrals above and below zero in the integral domain do not independently converge. (However, see Cauchy principal value

Cancellative semigroup (1,445 words) [view diff] exact match in snippet view article find links to article

cancellative. The procedure for doing this is similar to that of embedding an integral domain in a field (Clifford & Preston 1961, p. 34) – it is called the Grothendieck

Zariski's main theorem (1,620 words) [view diff] exact match in snippet view article find links to article

normal; in other words the completion of the local ring at x is a normal integral domain (Mumford 1999, III.9). Deligne's connectedness theorem Fulton–Hansen

Adjoint functors (9,958 words) [view diff] exact match in snippet view article find links to article

functor Field → Domm from fields has a left adjoint—it assigns to every integral domain its field of fractions. Polynomial rings. Let Ring* be the category

Farrell–Jones conjecture (2,216 words) [view diff] exact match in snippet view article find links to article

K^{top})=K_{*}(C_{r}(G))} The Kaplansky conjecture predicts that for an integral domain R {\displaystyle R} and a torsion-free group G {\displaystyle G} the

Tensor product of modules (8,467 words) [view diff] exact match in snippet view article find links to article

= f ( x ⊗ y ) {\displaystyle f'(x)(y)=f(x\otimes y)} . Let R be an integral domain with fraction field K. For any R-module M, K ⊗ R M ≅ K ⊗ R ( M / M

Glossary of representation theory (5,008 words) [view diff] exact match in snippet view article find links to article

function on conjugacy classes. cluster algebra A cluster algebra is an integral domain with some combinatorial structure on the generators, introduced in