Abstract
Let \(R\) be a unital K-algebra, where K is a commutative ring with unity. An idempotent \(e \in R\) is {\it left semicentral\/} if \(Re = eRe\), and \(R\) is {\it SCI-generated\/} if it is generated as a K-module by left semicentral idempotents. This paper develops the basic properties of SCI-generated algebras and characterizes those that are also prime, semiprime, primitive, or subdirectly irreducible. Minimal ideals and the socle of SCI-generated algebras are investigated. Conditions are found to describe a large class of SCI-generated algebras via generalized triangular matrix representations. SCI-generated piecewise domains are characterized. Examples are given that illustrate the breadth and diversity of the class of SCI-generated algebras.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
