Results 271 to 280 of about 725,736 (307)

Note on Primary Ideal Decompositions

Canadian Journal of Mathematics, 1966
Let R be a ring with a unity element. An ideal Q of R is called (right) primary if for ideals A and B of R, AB ⊂ Q and A ⊄ Q imply that Bn ⊂ Q for some positive integer n. If R satisfies the ascending chain condition for ideals (ACC), then R is said to have a Noetherian ideal theory if every ideal of R is an intersection of a finite number of primary ...
P. J. McCarthy
openaire   +2 more sources

Some of the next articles are maybe not open access.

Related searches:

Primary ideal decomposition

Lecture Notes in Computer Science, 1989
Kredel Heinz
exaly   +2 more sources

Algorithms for computing a primary ideal decomposition without producing intermediate redundant components

Journal of Symbolic Computation, 2011
In Noro (2010) we proposed an algorithm for computing a primary ideal decomposition by using the notion of a separating ideal and showed that it can efficiently decompose several examples which are hard to decompose using existing algorithms.
Masayuki Noro
exaly   +2 more sources

Valuation ideals and primary w-ideals

Frontiers of Mathematics in China, 2016
Let \(D\) be an integral domain. A nonzero ideal \(A\) of \(D\) is called a valuation ideal if there exists a valuation overring \(V\) of \(D\) such that \(AV\cap D=A\) [\textit{O. Zariski} and \textit{P. Samuel}, Commutative algebra. Vol. II. Princeton, N.J.-Toronto-London-New York: D (1960; Zbl 0121.27801)].
Chang, Gyu Whan, Kim, Hwankoo
openaire   +2 more sources

Primary Ideals and Prime Power Ideals

Canadian Journal of Mathematics, 1966
This paper is concerned with the ideal theory of a commutative ringR.We sayRhas Property (α) if each primary ideal inRis a power of its (prime) radical;Ris said to have Property (δ) provided every ideal inRis an intersection of a finite number of prime power ideals. In (2, Theorem 8, p.
Butts, H. S., Gilmer, R. W. jun.
openaire   +2 more sources

Primary Ideals and Valuation Ideals in Semigroups

Southeast Asian Bulletin of Mathematics, 2003
The authors give semigroup versions of two results (due to R. Gilmer and J. Ohm) about the relationship between primary ideals and valuation ideals in an integral domain. Let \(S\) be a nonzero submonoid of a torsionfree Abelian group. They first show that each valuation ideal of \(S\) is a primary ideal if and only if the set of nonunits of \(S\) is ...
Kanemitsu, Mitsuo, Tanaka, Hironao
openaire   +2 more sources

On Primary Ideals in Posets

Mathematica Slovaca, 2015
Abstract In this paper, we define the concepts of the radical of an ideal and a primary ideal in posets. Further, the analogue of the first and the second uniqueness theorems regarding primary decomposition of an ideal are obtained. In the last section, we prove that if an ideal in a poset Q has a minimal primary decomposition, then the
Joshi, Vinayak, Mundlik, Nilesh
openaire   +1 more source

Primary decomposition of homogeneous ideal in idealization of a module

Studia Scientiarum Mathematicarum Hungarica, 2018
Let R be a commutative Noetherian ring, M a finitely generated R-module, I an ideal of R and N a submodule of M such that IM ⫅ N. In this paper, the primary decomposition and irreducible decomposition of ideal I × N in the idealization of module R ⋉ M are given.
openaire   +1 more source

Primary Ideals in Prüfer Domains

Canadian Journal of Mathematics, 1966
A Prüfer domain is an integral domainDwith the property that for every proper prime idealPofDthe quotient ringDPis a valuation ring. Examples of such domains are valuation rings and Dedekind domains, a Dedekind domain being merely a noetherian Prüfer domain.
openaire   +1 more source

On quasi primary ideals and weakly quasi primary ideals

Summary: Let \(R\) be a commutative ring with identity. A proper ideal \(Q\) of \(R\) is called quasi primary (weakly quasi primary) if whenever \(ab\in Q\) (\(0\neq ab\in Q\)) for some \(a, b\in R\), then \(a\in\sqrt{Q}\) or \(b\in\sqrt{Q}\). In this paper, we study quasi primary (weakly quasi primary) ideals which are generalization of prime ideals ...
openaire   +1 more source