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On modules and rings with the restricted minimum condition

M. Tamer Koşan, Jan Žemlička (2015)

Colloquium Mathematicae

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 R R 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.

On near-ring ideals with ( σ , τ ) -derivation

Öznur Golbaşi, Neşet Aydin (2007)

Archivum Mathematicum

Let N be a 3 -prime left near-ring with multiplicative center Z , a ( σ , τ ) -derivation D on N is defined to be an additive endomorphism satisfying the product rule D ( x y ) = τ ( x ) D ( y ) + D ( x ) σ ( y ) for all x , y ∈ N , where σ and τ are automorphisms of N . A nonempty subset U of N will be called a semigroup right ideal (resp. semigroup left ideal) if U N ⊂ U (resp. N U ⊂ U ) and if U is both a semigroup right ideal and a semigroup left ideal, it be called a semigroup ideal. We prove the following results: Let D be a ( σ ,

On non singular p-inyective rings.

Yasuyuki Hirano (1994)

Publicacions Matemàtiques

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.

On nonstandard tame selfinjective algebras having only periodic modules

Jerzy Białkowski, Thorsten Holm, Andrzej Skowroński (2003)

Colloquium Mathematicae

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].

On ordered division rings

Ismail M. Idris (2001)

Colloquium Mathematicae

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...

On ordered division rings

Ismail M. Idris (2003)

Czechoslovak Mathematical Journal

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 → x a 2 for nonzero a , 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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