Semirings embedded in a completely regular semiring

M. K. Sen; S. K. Maity

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 143-148
  • ISSN: 0231-9721

Abstract

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Recently, we have shown that a semiring S is completely regular if and only if S is a union of skew-rings. In this paper we show that a semiring S satisfying a 2 = n a can be embedded in a completely regular semiring if and only if S is additive separative.

How to cite

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Sen, M. K., and Maity, S. K.. "Semirings embedded in a completely regular semiring." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 143-148. <http://eudml.org/doc/32356>.

@article{Sen2004,
abstract = {Recently, we have shown that a semiring $S$ is completely regular if and only if $ S$ is a union of skew-rings. In this paper we show that a semiring $S$ satisfying $a^2=na$ can be embedded in a completely regular semiring if and only if $S$ is additive separative.},
author = {Sen, M. K., Maity, S. K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {completely regular semiring; skew-ring; b-lattice; archimedean semiring; additive separative semiring; completely regular semirings; skew-rings; Archimedean semirings; additively separative semirings},
language = {eng},
number = {1},
pages = {143-148},
publisher = {Palacký University Olomouc},
title = {Semirings embedded in a completely regular semiring},
url = {http://eudml.org/doc/32356},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Sen, M. K.
AU - Maity, S. K.
TI - Semirings embedded in a completely regular semiring
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 143
EP - 148
AB - Recently, we have shown that a semiring $S$ is completely regular if and only if $ S$ is a union of skew-rings. In this paper we show that a semiring $S$ satisfying $a^2=na$ can be embedded in a completely regular semiring if and only if $S$ is additive separative.
LA - eng
KW - completely regular semiring; skew-ring; b-lattice; archimedean semiring; additive separative semiring; completely regular semirings; skew-rings; Archimedean semirings; additively separative semirings
UR - http://eudml.org/doc/32356
ER -

References

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  1. Clifford A. H., Preston G. B.: The algebraic theory of semigroups., Amer. Math. Soc., Providence Rhode Island, Vol. I, , 1961. (1961) MR0132791
  2. Grillet M. P., Semirings with a completely simple additive semigroup, J. Austral. Math. Soc. A 20 (1975), 257–267. (1975) Zbl0316.16039MR0491843
  3. Hebisch, U, Weinert H. J.: Semirings, Algebra Theory, Applications in Computer Science, Series in Algebra., Vol. 5, World Scientific, Singapore, , 1998. (1998) MR1704233
  4. Sen M. K., Maity S. K., Shum K. P., On completely regular semirings, (submitted). Zbl1115.16026

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