Notes on irreducible ideals
نویسندگان
چکیده
منابع مشابه
Weakly irreducible ideals
Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...
متن کاملweakly irreducible ideals
let $r$ be a commutative ring. the purpose of this article is to introduce a new class of ideals of r called weakly irreducible ideals. this class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. the relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...
متن کاملMATH 436 Notes: Ideals
An ideal K of R is a subset that is both a left ideal and a right ideal of R. For emphasis, we sometimes call it a two-sided ideal but the reader should understand that unless qualified, the word ideal will always refer to a two-sided ideal. The zero ideal (0) and the whole ring R are examples of two-sided ideals in any ring R. A (left)(right) ideal I such that I 6= R is called a proper (left)(...
متن کاملOn m - Primary Irreducible Ideals in F [ x ,
At the beginning of the last century F. S. Macaulay developed an elegant theory (see [4] Part IV) describing homogeneous ideals in polynomial rings. This theory makes the maximal-primary irriducible ideals I ⊂ Fýz1 , . . . , znü correspond to a single homogeneous inverse polynomial θI ∈ Fýz−1 1 , . . . , z−1 n ü. Macaulay’s theory has recently attracted attention in connection with problems ari...
متن کاملComputing Irreducible Decomposition of Monomial Ideals
The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic monomial ideals. The second one is an incremental algorithm, which computes decompositions of ideals by adding one generator at a time. Our analysis shows that th...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1985
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700009266