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Title: A note on orthodox additive inverse semirings (English)
Author: Sen, M. K.
Author: Maity, S. K.
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 43
Issue: 1
Year: 2004
Pages: 149-154
Summary lang: English
Category: math
Summary: We show in an additive inverse regular semiring $(S, +, \cdot )$ with $E^{\bullet }(S)$ as the set of all multiplicative idempotents and $E^+(S)$ as the set of all additive idempotents, the following conditions are equivalent: (i) For all $e, f \in E^{\bullet }(S)$, $ef \in E^+(S)$ implies $fe\in E^+(S)$. (ii) $(S, \cdot )$ is orthodox. (iii) $(S, \cdot )$ is a semilattice of groups. This result generalizes the corresponding result of regular ring. (English)
Keyword: additive inverse semirings
Keyword: regular semirings
Keyword: orthodox semirings
MSC: 16A78
MSC: 16E50
MSC: 16Y60
MSC: 20M07
MSC: 20M10
idZBL: Zbl 1067.16070
idMR: MR2124613
Date available: 2009-08-21T12:55:15Z
Last updated: 2012-05-04
Stable URL:
Reference: [1] Chaptal N.: Anneaux dont le demi groupe multiplicatif est inverse.C. R. Acad. Sci. Paris, Ser. A-B, 262 (1966), 247–277. Zbl 0133.29001, MR 0190177
Reference: [2] Golan J. S.: The Theory of Semirings with Applications in Mathematics, Theoretical Computer Science. : Pitman Monographs and Surveys in Pure and Applied Mathematics 54, Longman Scientific., 1992. MR 1163371
Reference: [3] Howie J. M., Introduction to the theory of semigroups. : Academic Press., 1976.
Reference: [4] Karvellas P. H.: Inverse semirings.J. Austral. Math. Soc. 18 (1974), 277–288. MR 0366991
Reference: [5] Zeleznekow J.: Regular semirings.Semigroup Forum 23 (1981), 119–136. MR 0641993


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