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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.29 n.1 Antofagasta mayo 2010

http://dx.doi.org/10.4067/S0716-09172010000100006 

Proyecciones Journal of Mathematics
Vol. 29, N° 1, pp. 49-56, May 2010.
Universidad Católica del Norte
Antofagasta - Chile


A NOTE ON THE UPPER RADICALS OF SEMINEARRINGS


Muhammad Zulfiqar

Govt. College University Lahore, Pakistan


Correspondencia a:


Abstract

In this paper we work in the class of seminearrings. Hereditary properties inherited by the lower radical generated by a class M have been considered in [2, 5, 6, 7, 9, 10, 12]. Here we consider the dual problem, namely strong properties which are inherited by the upper radical generated by a class M.

Keywords : Fuzzy subgroup, implication operator, subgroup degree

Subclass : [2000]03E72, 08A72, 20N25



References

[1] Birkenmeier, G. F., "SEMINEARRINGS AND NEARRINGS" induced by the circle operation, preprint, (1989).        [ Links ]

[2] Divinsky, N. J., "RINGS AND RADICALS", Toronto, (1965).        [ Links ]

[3] Golan, J. S., "THE THEORY OF SEMIRINGS WITH APPLICATIONS IN MATHEMATICS AND THEORETICAL COMPUTER SCIENCE", Pitman Monographs and Surveys in Pure and Applied Maths. 54, New-York, (1986).        [ Links ]

[4] Hebisch, U. and Weinert, H. J., "SEMIRINGS ALGEBRAIC THEORY AND APPLICATIONS IN COMPUTER SCIENCE", Vol. 5 (Singapore 1998).        [ Links ]

[5] Hoffman, A. E. and Leavitt, W. G., "Properties inherited by the Lower Radical", Port. Math. 27, pp. 63-66, (1968).        [ Links ]

[6] Krempa, N. J. and Sulinski, A., "Strong radical properties of alternative and associative rings", J. Algebra 17, pp. 369-388, (1971).        [ Links ]

[7] Leavitt, W. G., "Lower Radical Constructions', Rings, Modules and Radicals, Budapest, pp. 319-323, (1973).        [ Links ]

[8] Olson, D. M. and Jenksins, T. L., "Radical Theory for Hemirings", Jour. of Nat. Sciences and Math., Vol. 23, pp. 23-32, (1983).        [ Links ]

[9] Szasz, F. A., "RADICALS OF RINGS", Mathematical Institute Hungarian Academy of Sciences, (1981).        [ Links ]

[10] Tangeman, R. L. and Kreiling, D., "Lower radicals in non-associative rings", J. Australian Math. Soc. 14, pp. 419-423, (1972).        [ Links ]

[11] Hoorn, V. G. and Rootselaar, B., " Fundamental notions in the theory of seminerarings", Compositio Math. 18, pp. 65-78, (1966).        [ Links ]

[12] Wiegandt, R., "RADICAL AND SEMISIMPLE CLASSES OF RINGS", Queens University, Ontarto, Canada, (1974).        [ Links ]

[13] Weinert, H. J., "Seminearrings, seminearfield and their semigrouptheoretical background.", Semigroup Forum 24, pp. 231-254, (1982).        [ Links ]

[14] Weinert, H. J., "Extensions of seminearrings by semigroups of right quotients", Lect. Notes Math. 998, pp. 412-486, (1983).        [ Links ]

[15] Yusuf, S. M. and Shabir, M., "Radical classes and semisimple classes for hemiring", Studia Sci. Math. Hungarica 23, pp. 231-235, (1988).        [ Links ]

[16] Zulfiqar, M., "The sum of two radical classes of hemirings", Kyungpook Math. J. Vol. 43, pp. 371-374, (2003).        [ Links ]

Received : June 2009. Accepted : December 2009

Muhammad Zulfiqar
Department of Mathematics
Govt.College University Lahore
Pakistan
e-mail : mzulfiqarshafi@hotmail.com

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