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

Sunil K. Maity

Discussiones Mathematicae - General Algebra and Applications (2014)

  • Volume: 34, Issue: 1, page 75-84
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Sunil K. Maity. "On balanced order relations and the normal hull of completely simple semirings." Discussiones Mathematicae - General Algebra and Applications 34.1 (2014): 75-84. <http://eudml.org/doc/270496>.

@article{SunilK2014,
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.},
author = {Sunil K. Maity},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {skew-ring; Rees matrix semiring; balanced order relation; essential extension; normal extension; normal ideal; normal hull},
language = {eng},
number = {1},
pages = {75-84},
title = {On balanced order relations and the normal hull of completely simple semirings},
url = {http://eudml.org/doc/270496},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Sunil K. Maity
TI - On balanced order relations and the normal hull of completely simple semirings
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2014
VL - 34
IS - 1
SP - 75
EP - 84
AB - 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.
LA - eng
KW - skew-ring; Rees matrix semiring; balanced order relation; essential extension; normal extension; normal ideal; normal hull
UR - http://eudml.org/doc/270496
ER -

References

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  1. [1] M.K. Sen, S.K. Maity and H.J. Weinert, Completely simple semirings, Bull. Cal. Math. Soc 97 (2005) 163-172. Zbl1087.16031
  2. [2] M.K. Sen, S.K. Maity and K.P. Shum, On completely regular semirings, Bull. Cal. Math. Soc 98 (2006) 319-328. Zbl1115.16026
  3. [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. Zbl0316.16039
  4. [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. Zbl0513.20048
  5. [5] S.M. Goberstein, Balanced order relations on completely simple semigroups, Semigroup Forum 30 (1984) 121-124. doi: 10.1007/BF02573443. Zbl0548.06007

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