Results 241 to 250 of about 2,642,513 (283)

On wsq-primary ideals

Czechoslovak Mathematical Journal, 2023
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Aslankarayiğit Uğurlu, Emel, Bouba, El Mehdi, Tekir, Ünsal, Koç, Suat   +3 more
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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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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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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
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3-absorbing primary ideals

AIP Conference Proceedings, 2021
The notions of 3-absorbing primary ideals of ternary Γ-SO semiring were introduced in the following manuscript and obtain corresponding conditions and some characteristics of 3-absorbing primary ideals in ternary Γ-SO semirings.
Kothuru Bhagyalakshmi, V. Amarendra Babu
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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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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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