On Splitting Rings for Azumaya Skew Group Rings
Given a semiperfect two-sided noetherian ring Λ, we study two subcategories and of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories and , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.
In this paper we introduce the notion of the structure space of -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.
The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.
In this paper, we introduce the notion of ternary semi-integral domain and ternary semifield and study some of their properties.In particular we also investigate the maximal ideals of the ternary semiring Z¯₀.