integral domain
121Noether normalization lemma — In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced in (Noether 1926). A simple version states that for any field k, and any finitely generated commutative k algebra A, there exists a nonnegative integer …
122Idempotence — IPAEng|ˌaɪdɨmˈpoʊtəns describes the property of operations in mathematics and computer science which means that multiple applications of the operation does not change the result. The concept of idempotence arises in a number of places in abstract …
123Maximal ideal — In mathematics, more specifically in ring theory, a maximal ideal is an ideal which is maximal (with respect to set inclusion) amongst all proper ideals.[1][2] In other words, I is a maximal ideal of a ring R if I is an ideal of R, I ≠ R, and… …
124Krull dimension — In commutative algebra, the Krull dimension of a ring R, named after Wolfgang Krull (1899–1971), is the supremum of the number of strict inclusions in a chain of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. A… …
125Local ring — In abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called local behaviour , in the sense of functions defined on varieties or manifolds, or of… …
126Unit (ring theory) — In mathematics, a unit in a (unital) ring R is an invertible element of R , i.e. an element u such that there is a v in R with : uv = vu = 1 R , where 1 R is the multiplicative identity element.That is, u is an invertible element of the… …
127Height (ring theory) — In commutative algebra, the height of an prime ideal mathfrak{p} in a ring R is the number of strict inclusions in the longest chain of prime ideals contained in mathfrak{p} [Matsumura,Hideyuki: Commutative Ring Theory ,page 30 31,1989 ] . Then… …
128Characteristic (algebra) — In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring s multiplicative identity element (1) in a sum to get the additive identity element (0); the ring is said… …
