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.
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Birkenmeier, G.F., Heatherly, H.E., Kim, J.Y. et al. Algebras Generated by Semicentral Idempotents. Acta Mathematica Hungarica 95, 101–114 (2002). https://doi.org/10.1023/A:1015616301342
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DOI: https://doi.org/10.1023/A:1015616301342