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Locally adequate semigroup algebras

Yingdan Ji, Yanfeng Luo (2016)

Open Mathematics

We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J* 0 - 𝒥 * -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ* * -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description...

Loewy coincident algebra and Q F -3 associated graded algebra

Hiroyuki Tachikawa (2009)

Czechoslovak Mathematical Journal

We prove that an associated graded algebra R G of a finite dimensional algebra R is Q F (= selfinjective) if and only if R is Q F and Loewy coincident. Here R is said to be Loewy coincident if, for every primitive idempotent e , the upper Loewy series and the lower Loewy series of R e and e R coincide. Q F -3 algebras are an important generalization of Q F algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra R , the associated graded algebra...

L-zero-divisor graphs of direct products of L-commutative rings

S. Ebrahimi Atani, M. Shajari Kohan (2011)

Discussiones Mathematicae - General Algebra and Applications

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-ziro-divisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

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