# 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

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topAnjan 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 -

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