On a variety of commutative multiplicatively idempotent semirings |
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| Authors: | Ivan?Chajda,Helmut?L?nger mailto:helmut.laenger@tuwien.ac.at" title=" helmut.laenger@tuwien.ac.at" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
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| Affiliation: | 1.Department of Algebra and Geometry, Faculty of Science,Palacky University Olomouc,Olomouc,Czech Republic;2.Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry,TU Wien,Vienna,Austria |
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| Abstract: | ![]()
We prove that the variety ({{mathscr {V}}}) of commutative multiplicatively idempotent semirings satisfying (x+y+xyzapprox x+y) is generated by a single three-element semiring. Moreover, we describe a normal form system for terms in ({{mathscr {V}}}) and we show that the word problem in ({{mathscr {V}}}) is solvable. Although ({{mathscr {V}}}) is locally finite, it is residually big. |
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