Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

Anjan Kumar Bhuniya; Kanchan Jana

Discussiones Mathematicae - General Algebra and Applications (2014)

  • Volume: 34, Issue: 1, page 27-43
  • ISSN: 1509-9415

Abstract

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Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.

How to cite

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Anjan Kumar Bhuniya, and Kanchan Jana. "Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct." Discussiones Mathematicae - General Algebra and Applications 34.1 (2014): 27-43. <http://eudml.org/doc/270663>.

@article{AnjanKumarBhuniya2014,
abstract = {Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.},
author = {Anjan Kumar Bhuniya, Kanchan Jana},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {quasi k-ideal; strong quasi k-ideal; strong quasi k-simple; t-k-simple; t-k-Archimedean},
language = {eng},
number = {1},
pages = {27-43},
title = {Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct},
url = {http://eudml.org/doc/270663},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Anjan Kumar Bhuniya
AU - Kanchan Jana
TI - Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2014
VL - 34
IS - 1
SP - 27
EP - 43
AB - Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.
LA - eng
KW - quasi k-ideal; strong quasi k-ideal; strong quasi k-simple; t-k-simple; t-k-Archimedean
UR - http://eudml.org/doc/270663
ER -

References

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