ArticleOriginal scientific text
Title
On balanced order relations and the normal hull of completely simple semirings
Authors 1
Affiliations
- Department of Mathematics, University of Burdwan, Golapbag, Burdwan - 713104 West Bengal, India
Abstract
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.
Keywords
skew-ring, Rees matrix semiring, balanced order relation, essential extension, normal extension, normal ideal, normal hull
Bibliography
- M.K. Sen, S.K. Maity and H.J. Weinert, Completely simple semirings, Bull. Cal. Math. Soc 97 (2005) 163-172.
- M.K. Sen, S.K. Maity and K.P. Shum, On completely regular semirings, Bull. Cal. Math. Soc 98 (2006) 319-328.
- M.P. Grillet, Semirings with a completely simple additive semigroup, J. Austral. Math. Soc.(Series A) 20 (1975) 257-267. doi: 10.1017/S1446788700020607.
- 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.
- S.M. Goberstein, Balanced order relations on completely simple semigroups, Semigroup Forum 30 (1984) 121-124. doi: 10.1007/BF02573443.
Pages:
75-84
Main language of publication
English
Received
2013-08-22
Accepted
2013-10-30
Published
2014
DOI: 10.7151/dmgaa.1218
Exact and natural sciences