On balanced order relations and the normal hull of completely simple semirings

• Autorzy: Sunil K. Maity
• Języki publikacji: EN

Abstrakty

EN

In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under multiplication. In this paper we characterize all the balanced order relations on completely simple semirings. Also we study the normal hull of a completely simple semiring.

Słowa kluczowe

EN

skew-ring; Rees matrix semiring; balanced order relation; essential extension; normal extension; normal ideal; normal hull

Kategorie tematyczne

• 20M10: General structure theory
• 20M07: Varieties and pseudovarieties of semigroups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 75-84

Daty

wydano

2014

otrzymano

2013-08-22

poprawiono

2013-10-30

Twórcy

autor

Sunil K. Maity

• Department of Mathematics, University of Burdwan, Golapbag, Burdwan - 713104 West Bengal, India

Bibliografia

• [1] M.K. Sen, S.K. Maity and H.J. Weinert, Completely simple semirings, Bull. Cal. Math. Soc 97 (2005) 163-172.
• [2] M.K. Sen, S.K. Maity and K.P. Shum, On completely regular semirings, Bull. Cal. Math. Soc 98 (2006) 319-328.
• [3] M.P. Grillet, Semirings with a completely simple additive semigroup, J. Austral. Math. Soc.(Series A) 20 (1975) 257-267. doi: 10.1017/S1446788700020607.
• [4] M. Petrich and N. Reilly, The normal hull of a completely simple semigroup, J. Algebra 81 (1983) 232-257. doi: 10.1016/0021-8693(83)90218-1.
• [5] S.M. Goberstein, Balanced order relations on completely simple semigroups, Semigroup Forum 30 (1984) 121-124. doi: 10.1007/BF02573443.

Identyfikatory

DOI

10.7151/dmgaa.1218