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02-01-2019 | Foundations

On a hereditarily finitely based ai-semiring variety

Authors: Miaomiao Ren, Lingli Zeng

Published in: Soft Computing | Issue 16/2019

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Abstract

Let \(\mathbf{W}\) denote the join of the ai-semiring variety axiomatized by \(x^2\approx x\) and the ai-semiring variety axiomatized by \(xy\approx zt\). We show that the lattice of subvarieties of \(\mathbf{W}\), \(\mathcal{L}(\mathbf{W})\), is a distributive lattice of order 312. Also, all members of this variety are finitely based and finitely generated. Thus, \(\mathbf{W}\) is hereditarily finitely based.

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Title: On a hereditarily finitely based ai-semiring variety
Authors: Miaomiao Ren
Lingli Zeng
Publication date: 02-01-2019
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 16/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-018-03719-0

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