The search session has expired. Please query the service again.
Displaying 141 –
160 of
181
Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x ∈ M there exists a homomorphism F: M → R such that f(x) = x. Let Q be a left R-module and h: Q → M a homomorphism. We call h locally split if for every x ∈ M there exists a homomorphism g: M → Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:(1) M is Zelmanowitz-regular.(2) every homomorphism into M...
An exchange ring is strongly separative provided that for all finitely generated projective right -modules and , . We prove that an exchange ring is strongly separative if and only if for any corner of , implies that there exist such that and if and only if for any corner of , implies that there exists a right invertible matrix . The dual assertions are also proved.
A -ring is strongly 2-nil--clean if every element in is the sum of two projections and a nilpotent that commute. Fundamental properties of such -rings are obtained. We prove that a -ring is strongly 2-nil--clean if and only if for all , is strongly nil--clean, if and only if for any there exists a -tripotent such that is nilpotent and , if and only if is a strongly -clean SN ring, if and only if is abelian, is nil and is -tripotent. Furthermore, we explore the structure...
Certaines relations binaires sont définies sur les demi-groupes et les demi-groupes à involution. On examine comment elles peuvent en ordonner les éléments: notamment les idempotents, les éléments réguliers au sens de von Neumann, ceux qui possédent un inverse ponctuel ou de Moore-Penrose ; et en fonction aussi de conditions sur l'involution. Ces relations peuvent alors coïncider avec les ordres naturels des idempotents et des demi-groupes inverses, avec les ordres de Drazin et de Hartwig : elles...
A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K. C. O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring.
We give a new proof of the main result of [1] which does not use the classification of the finite simple groups.
In this paper, we prove that unit ideal-stable range condition is right and left symmetric.
Currently displaying 141 –
160 of
181