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Keywords:
bi-ideal-simple; semiring; zeropotent
bi-ideal-simple; semiring; zeropotent
Summary:
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.
References:
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[2] El Bashir R., Hurt J., Jančařík A., Kepka T.: Simple commutative semirings. J. Algebra 236 (2001), 277-306. MR 1808355 | Zbl 0976.16034
[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). MR 1163371
[4] Hebisch U., Weinert H.J.: Halbringe. Algebraische Theorie und Anwendungen in der Informatik. Teubner Stuttgart (1993). MR 1311247 | Zbl 0829.16035
[5] Hutehins H.C., Weinert H.J.: Homomorphisms and kernels of semifields. Period. Math. Hungar. 21 (1990), 113-152. MR 1070951
[6] Koch H.: Über Halbkörper, die in algebraischen Zahlkörpern enhalten sind. Acta Math. Acad. Sci. Hungar. 15 (1964), 439-444. MR 0168609
[7] Mitchell S.S., Fenoglio P.B.: Congruence-free commutative semirings. Semigroup Forum 37 (1988), 79-91. MR 0929445 | Zbl 0636.16020
[8] Monico C.: On finite congruence-simple semirings. J. Algebra 271 (2004), 846-854. MR 2025553 | Zbl 1041.16041
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