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Weak multiplication modules

Abdelmalek Azizi (2003)

Czechoslovak Mathematical Journal

In this paper we characterize weak multiplication modules.

Weak multiplication modules over a pullback of Dedekind domains

S. Ebrahimi Atani, F. Farzalipour (2009)

Colloquium Mathematicae

Let R be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finite-dimensional over R/Rad(R). We also establish a connection between the weak multiplication modules and the pure-injective modules over such domains.

When is each proper overring of R an S(Eidenberg)-domain?

Noômen Jarboui (2002)

Publicacions Matemàtiques

A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dimv(R) = 2 and L = qf(R).

When is every order ideal a ring ideal?

Melvin Henriksen, Suzanne Larson, Frank A. Smith (1991)

Commentationes Mathematicae Universitatis Carolinae

A lattice-ordered ring is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f -rings such that / 𝕀 is contained in an f -ring with an identity element that is a strong order unit for some nil l -ideal 𝕀 of . In particular, if P ( ) denotes the set of nilpotent elements of the f -ring , then is an OIRI-ring if and only if / P ( ) is contained in an f -ring with an identity element that is a strong order unit....

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