Displaying similar documents to “Errata to the paper 'On the ε-theorems' (Fund. Math. 43, p. 156-165)”

z⁰-Ideals and some special commutative rings

Karim Samei (2006)

Fundamenta Mathematicae

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In a commutative ring R, an ideal I consisting entirely of zero divisors is called a torsion ideal, and an ideal is called a z⁰-ideal if I is torsion and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We prove that in large classes of rings, say R, the following results hold: every z-ideal is a z⁰-ideal if and only if every element of R is either a zero divisor or a unit, if and only if every maximal ideal in R (in general, every prime z-ideal)...

On commutative rings whose prime ideals are direct sums of cyclics

M. Behboodi, A. Moradzadeh-Dehkordi (2012)

Archivum Mathematicum

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In this paper we study commutative rings R whose prime ideals are direct sums of cyclic modules. In the case R is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that for a local ring ( R , ) , the following statements are equivalent: (1) Every prime ideal of R is a direct sum of cyclic R -modules; (2) = λ Λ R w λ where Λ is an index set and R / Ann ( w λ ) is a principal ideal ring for each λ Λ ; (3) Every prime ideal of R is a direct...

Ideals of BCI-algebras and their Properties

Chenglong Wu, Yuzhong Ding (2008)

Formalized Mathematics

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In this article three classes of ideals are discussed: associative ideals, commutative ideals, implicative ideals and positive implicative ideals, and their elementary properties. Some of their properties and the relationships between them have not been proven yet, and will be completed in the following article.MML identifier: BCIIDEAL, version: 7.8.10 4.99.1005