منابع مشابه
Rings for which every simple module is almost injective
We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...
متن کاملrings for which every simple module is almost injective
we introduce the class of “right almost v-rings” which is properly between the classes of right v-rings and right good rings. a ring r is called a right almost v-ring if every simple r-module is almost injective. it is proved that r is a right almost v-ring if and only if for every r-module m, any complement of every simple submodule of m is a direct summand. moreover, r is a right almost v-rin...
متن کاملProjective Representations I. Projective lines over rings
We discuss representations of the projective line over a ring R with 1 in a projective space over some (not necessarily commutative) field K. Such a representation is based upon a (K,R)-bimodule U . The points of the projective line over R are represented by certain subspaces of the projective space P(K,U ×U) that are isomorphic to one of their complements. In particular, distant points go over...
متن کاملFuzzy projective modules and tensor products in fuzzy module categories
Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...
متن کاملCommutative rings in which every finitely generated ideal is quasi-projective
This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3 investigates the correlation with well-known Prüfer conditions; namely, we prove that this class of rings stands strictly between the two classes of arithmetical...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1992
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1992.128346