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$I$-compactness and prime ideals [PDF]
Publicationes Mathematicae Debrecen, 2022 Ein Ring \(R\) mit Einselement heißt ein rechter Kettenring, wenn die Menge der Rechtsideale durch Inklusion linear geordnet ist. Ist \(I\) ein Rechtsideal von \(K\), so heißt \(R\) \(I\)-kompakt, wenn die kanonische Abbildung von \(R\) in den inversen Limes von \(R/I_ \lambda\) für jede Familie \(\{\lambda\mid \lambda\in \Lambda\}\) von Rechtsidealen \
Törner, Günter, Brungs, H.H.
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Primary Ideals and Prime Power Ideals
Canadian Journal of Mathematics, 1966This 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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Algebra Colloquium, 2010
It is well known that there are several non-equivalent types of prime near-rings which are all equivalent in the case of associative rings. In this paper we introduce various characterizations of prime modules in a zero-symmetric near-ring R. The connection of a prime R-ideal P of a module M and the ideal (P:M) of the near-ring R is also investigated.
Juglal, S. +2 more
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It is well known that there are several non-equivalent types of prime near-rings which are all equivalent in the case of associative rings. In this paper we introduce various characterizations of prime modules in a zero-symmetric near-ring R. The connection of a prime R-ideal P of a module M and the ideal (P:M) of the near-ring R is also investigated.
Juglal, S. +2 more
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Fuzzy prime ideals and prime fuzzy ideals
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fuzzy Sets and Systems, 1996
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Garmendia, Alfonso +2 more
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Garmendia, Alfonso +2 more
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Rough prime ideals and rough fuzzy prime ideals in semigroups
Information Sciences, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao, Qi-Mei, Zhang, Zhen-Liang
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JP Journal of Algebra, Number Theory and Applications, 2017
Summary: Let \(R\) be a domain with the quotient field \(K\). A strongly prime ideal in \(R\) is any prime ideal \(P\) of \(R\) such that whenever \(x\) and \(y\) are elements of \(K\) with \(xRy\subset P\), either \(x\in P\) or \(y\in P\). A domain \(R\) is called fully strongly prime if every prime ideal of \(R\) is strongly prime.
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Summary: Let \(R\) be a domain with the quotient field \(K\). A strongly prime ideal in \(R\) is any prime ideal \(P\) of \(R\) such that whenever \(x\) and \(y\) are elements of \(K\) with \(xRy\subset P\), either \(x\in P\) or \(y\in P\). A domain \(R\) is called fully strongly prime if every prime ideal of \(R\) is strongly prime.
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Prime elements from prime ideals
Order, 1985In the summer of 1984 A. R. Blass proved that the ''Almost Maximal Ideal Theorem'' which had been introduced by the reviewer [Fundam. Math. 123, 197-209 (1984; Zbl 0552.06004)] - and which he had previously believed to be a choice principle intermediate between the Prime Ideal Theorem and the Axiom of Choice - was in fact logically equivalent to the ...
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