Semicentral Reduced Algebras
An idempotent e of an algebra R is left semicentral if Re = eRe. If 0 and 1 are the only left semicentral idempotents in R, then R is called semicentral reduced. Recent results on generalized triangular matrix algebras and semicentral reduced algebras are surveyed. New results are provided for endomorphism algebras of modules and for semicentral reduced algebras. In particular, semicentral reduced rings which are right FPF, right nonsingular, or left perfect are described.
KeywordsLeft Ideal Prime Ring Primitive Idempotent Trivial Extension Orthogonal Idempotent
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- G. F. Birkenmeier, B. J. Müller, and S. T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summand, Preprint.Google Scholar
- C. Faith, Injective quotient rings of commutative rings, Module Theory, Lecture Notes in Math. 700, Springer-Verlag, Heidelberg, New York (1979), 151–203.Google Scholar