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Onα-almost Artinian modules

Maryam Davoudian, Ahmad Halali, Nasrin Shirali (2016)

Open Mathematics

In this article we introduce and study the concept of α-almost Artinian modules. We show that each α-almost Artinian module M is almost Artinian (i.e., every proper homomorphic image of M is Artinian), where α ∈ {0,1}. Using this concept we extend some of the basic results of almost Artinian modules to α-almost Artinian modules. Moreover we introduce and study the concept of α-Krull modules. We observe that if M is an α-Krull module then the Krull dimension of M is either α or α + 1.

Orbit algebras and periodicity

Petter Andreas Bergh (2009)

Colloquium Mathematicae

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation type.

Orbit algebras that are invariant under stable equivalences of Morita type

Zygmunt Pogorzały (2014)

Open Mathematics

In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.

Orderings and preorderings in rings with involution

Ismail Idris (2000)

Colloquium Mathematicae

The notions of a preordering and an ordering of a ring R with involution are investigated. An algebraic condition for the existence of an ordering of R is given. Also, a condition for enlarging an ordering of R to an overring is given. As for the case of a field, any preordering of R can be extended to some ordering. Finally, we investigate the class of archimedean ordered rings with involution.

Ordinary selfdistributive rings

Sobhy Ghoneim, Marian Kechlibar, Tomáš Kepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Left selfdistributive rings (i.e., x y z = x y x z ) which are semidirect sums of boolean rings and rings nilpotent of index at most 3 are studied.

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