On the structure of subalgebra systems of idempotent entropic algebras
type: Item
instance of: scholarly article
title: On the structure of subalgebra systems of idempotent entropic algebras
zbMATH Open document ID: 0663.08002
DOI: 10.1016/0021-8693(89)90198-1
author: Anna Romanowska
author: J. D. H. Smith
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: The paper continues the study of subalgebra systems initiated in the preceding one (see Zbl 0663.08001). In the present part the subalgebra systems of idempotent entropic algebras (or IEO-semilattices) are investigated by means of various decomposition methods. The attention is focused on the decomposition of meet-distributive bisemilattices since these algebras play an essential role in the structure of IEO- semilattices. Simultaneously the corresponding methods for recovering the original idempotent entropic algebras from their decompositions are given. It is shown that the generalized Płonka sum is a useful tool for reconstruction of some idempotent entropic algebras.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 06A12
zbMATH DE Number: 4083698
zbMATH Keywords: idempotent-entropic operator semilattice
zbMATH Keywords: subalgebra systems
zbMATH Keywords: idempotent entropic algebras
zbMATH Keywords: decomposition
zbMATH Keywords: meet-distributive bisemilattices
zbMATH Keywords: generalized Płonka sum
reviewed by: Jaromír Duda
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90198-1
OpenAlex ID: W2085855567
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description: scientific article; zbMATH DE number 4083698