Bi-ideal-simple semirings

Václav Flaška; Tomáš Kepka; Jan Šaroch

Commentationes Mathematicae Universitatis Carolinae (2005)

• Volume: 46, Issue: 3, page 391-397
• ISSN: 0010-2628

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Abstract

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Commutative congruence-simple semirings were studied in [2] and [7] (but see also [1], [3]--[6]). The non-commutative case almost (see [8]) escaped notice so far. Whatever, every congruence-simple semiring is bi-ideal-simple and the aim of this very short note is to collect several pieces of information on these semirings.

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Flaška, Václav, Kepka, Tomáš, and Šaroch, Jan. "Bi-ideal-simple semirings." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 391-397. <http://eudml.org/doc/249546>.

@article{Flaška2005,
abstract = {Commutative congruence-simple semirings were studied in [2] and [7] (but see also [1], [3]--[6]). The non-commutative case almost (see [8]) escaped notice so far. Whatever, every congruence-simple semiring is bi-ideal-simple and the aim of this very short note is to collect several pieces of information on these semirings.},
author = {Flaška, Václav, Kepka, Tomáš, Šaroch, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {bi-ideal-simple; semiring; zeropotent; bi-ideal-simple semirings; zeropotent semirings; congruence-simple semirings; congruences},
language = {eng},
number = {3},
pages = {391-397},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Bi-ideal-simple semirings},
url = {http://eudml.org/doc/249546},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Flaška, Václav
AU - Kepka, Tomáš
AU - Šaroch, Jan
TI - Bi-ideal-simple semirings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 391
EP - 397
AB - Commutative congruence-simple semirings were studied in [2] and [7] (but see also [1], [3]--[6]). The non-commutative case almost (see [8]) escaped notice so far. Whatever, every congruence-simple semiring is bi-ideal-simple and the aim of this very short note is to collect several pieces of information on these semirings.
LA - eng
KW - bi-ideal-simple; semiring; zeropotent; bi-ideal-simple semirings; zeropotent semirings; congruence-simple semirings; congruences
UR - http://eudml.org/doc/249546
ER -

References

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2. El Bashir R., Hurt J., Jančařík A., Kepka T., Simple commutative semirings, J. Algebra 236 (2001), 277-306. (2001) Zbl0976.16034MR1808355
3. Golan J., The Theory of Semirings with Application in Math. and Theoretical Computer Science, Pitman Monographs and Surveys in Pure and Applied Mathematics 54 Longman, Harlow (1992). (1992) MR1163371
4. Hebisch U., Weinert H.J., Halbringe. Algebraische Theorie und Anwendungen in der Informatik, Teubner Stuttgart (1993). (1993) Zbl0829.16035MR1311247
5. Hutehins H.C., Weinert H.J., Homomorphisms and kernels of semifields, Period. Math. Hungar. 21 (1990), 113-152. (1990) MR1070951
6. Koch H., Über Halbkörper, die in algebraischen Zahlkörpern enhalten sind, Acta Math. Acad. Sci. Hungar. 15 (1964), 439-444. (1964) MR0168609
7. Mitchell S.S., Fenoglio P.B., Congruence-free commutative semirings, Semigroup Forum 37 (1988), 79-91. (1988) Zbl0636.16020MR0929445
8. Monico C., On finite congruence-simple semirings, J. Algebra 271 (2004), 846-854. (2004) Zbl1041.16041MR2025553

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