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A module M satisfies the restricted minimum condition if M/N is artinian for every essential submodule N of M. A ring R is called a right RM-ring whenever satisfies the restricted minimum condition as a right module. We give several structural necessary conditions for particular classes of RM-rings. Furthermore, a commutative ring R is proved to be an RM-ring if and only if R/Soc(R) is noetherian and every singular module is semiartinian.
We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.
We investigate some properties of -submodules. More precisely, we find a necessary and sufficient condition for every proper submodule of a module to be an -submodule. Also, we show that if is a finitely generated -module and is a prime ideal of , then has -submodule. Moreover, we define the notion of -submodule, which is a generalization of the notion of -submodule. We find some characterizations of -submodules and we examine the way the aforementioned notions are related to each...
Let be a -prime left near-ring with multiplicative center , a -derivation on is defined to be an additive endomorphism satisfying the product rule for all , where and are automorphisms of . A nonempty subset of will be called a semigroup right ideal (resp. semigroup left ideal) if (resp. ) and if is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let be a
A ring R is said to be left p-injective if, for any principal left ideal I of R, any left R-homomorphism I into R extends to one of R into itself. In this note left nonsingular left p-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left p-injective rings of bounded index is investigated.
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as in the commutative...
Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel’s axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under for nonzero , instead of requiring that positive elements have a positive product. In this work, this type of ordering is studied in the case of a division ring. It is shown that it actually behaves the same as in the commutative...
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