Results 261 to 270 of about 23,078 (295)

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 ...
Mitsuo Kanemitsu
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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.
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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
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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
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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.
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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 ...
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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.
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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 ...
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On the Primary Decomposition of k-Ideals and Fuzzy k-Ideals in Semirings

Fuzzy Information and Engineering, 2021
Madhu Dadhwal, S Kar
exaly  

WEAKLY PRIMARY IDEAL AND Φ-PRIMARY IDEAL IN AMALGAMATED ALGEBRA ALONG AN IDEAL

JP Journal of Algebra, Number Theory and Applications, 2020
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