Clifford semifields

Mridul K. Sen; Sunil K. Maity; Kar-Ping Shum

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 1, page 125-135
  • ISSN: 1509-9415

Abstract

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It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.

How to cite

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Mridul K. Sen, Sunil K. Maity, and Kar-Ping Shum. "Clifford semifields." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 125-135. <http://eudml.org/doc/287642>.

@article{MridulK2004,
abstract = {It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.},
author = {Mridul K. Sen, Sunil K. Maity, Kar-Ping Shum},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {skew-ring; Clifford semiring; Clifford semidomain; Clifford semifield; Artinian Clifford semiring; skew-rings; Clifford semirings; semilattices; Clifford semidomains; Clifford semifields},
language = {eng},
number = {1},
pages = {125-135},
title = {Clifford semifields},
url = {http://eudml.org/doc/287642},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Mridul K. Sen
AU - Sunil K. Maity
AU - Kar-Ping Shum
TI - Clifford semifields
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 1
SP - 125
EP - 135
AB - It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.
LA - eng
KW - skew-ring; Clifford semiring; Clifford semidomain; Clifford semifield; Artinian Clifford semiring; skew-rings; Clifford semirings; semilattices; Clifford semidomains; Clifford semifields
UR - http://eudml.org/doc/287642
ER -

References

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  1. [1] D.M. Burton, A First Course in Rings and Ideals, Addison-Wesley Publishing Company, Reading, MA, 1970. Zbl0204.05601
  2. [2] M.P. Grillet, Semirings with a completely simple additive semigroup, J. Austral. Math. Soc. (Series A) 20 (1975), 257-267. Zbl0316.16039
  3. [3] P.H. Karvellas, Inverse semirings, J. Austral. Math. Soc. 18 (1974), 277-288. 
  4. [4] M.K. Sen, S.K. Maity and K.-P. Shum, Semisimple Clifford semirings, 'Advances in Algebra', World Scientific, Singapore, 2003, 221-231. 
  5. [5] M.K. Sen, S.K. Maity and K.-P. Shum, Clifford semirings and generalized Clifford semirings, Taiwanese J. Math., to appear. Zbl1091.16028
  6. [6] M.K. Sen, S.K. Maity and K.-P. Shum, On Completely Regular Semirings, Taiwanese J. Math., submitted. 
  7. [7] J. Zeleznekow, Regular semirings, Semigroup Forum, 23 (1981), 119-136. 

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