Green’s -relation for the multiplicative reduct of an idempotent semiring
Francis J. Pastijn; Xian Zhong Zhao
Archivum Mathematicum (2000)
- Volume: 036, Issue: 2, page 77-93
- ISSN: 0044-8753
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topPastijn, Francis J., and Zhao, Xian Zhong. "Green’s $\mathcal {D}$-relation for the multiplicative reduct of an idempotent semiring." Archivum Mathematicum 036.2 (2000): 77-93. <http://eudml.org/doc/248520>.
@article{Pastijn2000,
abstract = {The idempotent semirings for which Green’s $\{\mathcal \{D\}\}$-relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the $\{\mathcal \{D\}\}$-relation on the multiplicative reduct is the least lattice congruence.},
author = {Pastijn, Francis J., Zhao, Xian Zhong},
journal = {Archivum Mathematicum},
keywords = {idempotent semiring; variety; Green relations; band; bisemilattice; idempotent semirings; varieties; Green relations; bands; bisemilattices; identities; lattice congruences},
language = {eng},
number = {2},
pages = {77-93},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Green’s $\mathcal \{D\}$-relation for the multiplicative reduct of an idempotent semiring},
url = {http://eudml.org/doc/248520},
volume = {036},
year = {2000},
}
TY - JOUR
AU - Pastijn, Francis J.
AU - Zhao, Xian Zhong
TI - Green’s $\mathcal {D}$-relation for the multiplicative reduct of an idempotent semiring
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 2
SP - 77
EP - 93
AB - The idempotent semirings for which Green’s ${\mathcal {D}}$-relation on the multiplicative reduct is a congruence relation form a subvariety of the variety of all idempotent semirings. This variety contains the variety consisting of all the idempotent semirings which do not contain a two-element monobisemilattice as a subsemiring. Various characterizations will be given for the idempotent semirings for which the ${\mathcal {D}}$-relation on the multiplicative reduct is the least lattice congruence.
LA - eng
KW - idempotent semiring; variety; Green relations; band; bisemilattice; idempotent semirings; varieties; Green relations; bands; bisemilattices; identities; lattice congruences
UR - http://eudml.org/doc/248520
ER -
References
top- Howie J. M., Fundamentals of Semigroup Theory, Oxford Science Publications, Oxford, 1995. (1995) Zbl0835.20077MR1455373
- McKenzie R., and A. Romanowska, Varieties of -distributive bisemilattices, Contributions to General Algebra, (Proc. Klagenfurt Conf., Klagenfurt 1978), 213–218, Heyn, Klagenfurt, 1979. (1978) MR0537422
- Pastijn F., and Y. Q. Guo, The lattice of idempotent distributive semiring varieties, Science in China (Series A) 42 (8) (1999), 785–804. (1999) MR1738550
- Sen M. K., Guo Y. Q., and K. P. Shum, A class of idempotent semirings, preprint. MR1828821
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