PDF

Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 107-117
DOI: https://doi.org/10.7151/dmgaa.1050

ON p-SEMIRINGS

Branka Budimirović, Vjekoslav Budimirović Higher Technological School Narodnih Heroja 10, 15000 Sabac, Yugoslavia

Branimir Seselja Institute of Mathematics, University of Novi Sad Trg D. Obradovića 4, 21000 Novi Sad, Yugoslavia e-mail: seselja@im.ns.ac.yu

Abstract

A class of semirings, so called p-semirings, characterized by a natural number p is introduced and basic properties are investigated. It is proved that every p-semiring is a union of skew rings. It is proved that for some p-semirings with non-commutative operations, this union contains rings which are commutative and possess an identity. 

Keywords and phrases: semiring, p-semiring, p-semigroup, anti-inverse semigroup, union of rings, skew ring.

2000 AMS Mathematics Subject Classification: Primary 16Y60, Secondary 16S99.

References

[1] B. Budimirović, On a class of p-semirings, M.Sc. Thesis, Faculty of Sciences, University of Novi Sad, 2001.

[2] V. Budimirović, A Contribution to the Theory of Semirings, Ph.D. Thesis, Fac. of Sci., University of Novi Sad, Novi Sad, 2001.

[3] V. Budimirović, On p-semigroups, Math. Moravica 4 (2000), 5-20.

[4] V. Budimirović and B. Seselja, Operators H, S and P in the classes of p-semigroups and p-semirings, Novi Sad J. Math. 32 (2002), 127-132.

[5] S. Bogdanović, S. Milić and V. Pavlović, Anti-inverse semigroups, Publ. Inst. Math. (Beograd) (N.S.) 24 (38) (1978), 19-28.

[6] K. G azek, A guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences, Kluwer Acad. Publ. Dordrecht 2002.

[7] J.S. Golan, The theory of semirings with applications in mathematics and theoretical computer sciences, Longman Scientific & Technical, Harlow 1992.

[8] U. Hebisch and H.J. Weinert, Semirings, Algebraic theory and applications in mathematics and computer sciences, World Scientific, Singapore 1999.

[9] I.N. Herstein, Wedderburn's Theorem and a Theorem of Jacobson, Amer. Math. Monthly 68 (1961), 249-251.

Received 28 January 20002
Revised 7 October 20002