[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2008.45.4.757

A NOTE ON LOWER RADICALS OF HEMIRINGS

Zulfiqar, Muhammad (DEPARTMENT OF MATHEMATICS GOVT. COLLEGE UNIVERSITY LAHORE)

Publication Information

Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 757-762 More about this Journal

Abstract

In this paper, we generalize a few results of [7, 10] for lower radical classes of rings, by using the limit ordinal construction for lower radical classes of hemirings.

Keywords

hemiring; radical classes; universal class; semisimple class; homomorphically closed; p-semi-ideal; k-ideal; hereditary class; lower radical;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	Y. L. Lee, On the construction of lower radical properties, Pacific J. Math. 28 (1969), 393-395 DOI
2	J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, Pitman Monographs and Surveys in Pure and Applied Mathematics, 54. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992
3	H. J. le Roux and G. A. P. Heyman, A note on the lower radical, Publ. Math. Debrecen 28 (1981), no. 1-2, 11-13
4	Y. L. Lee, On the construction of upper radical properties, Proc. Amer. Math. Soc. 19 (1968), 1165-1166
5	Y. L. Lee and R. E. Propes, On intersections and unions of radical classes, J. Austral. Math. Soc. 13 (1972), 354-356 DOI
6	D. M. Olson and T. L. Jenksins, Radical theory for hemirings, J. Natur. Sci. Math. 23 (1983), no. 1, 23-32
7	U. Hebisch and H. J. Weinert, Semirings: algebraic theory and applications in computer science, Translated from the 1993 German original. Series in Algebra, 5. World Scientific Publishing Co., Inc., River Edge, NJ, 1998
8	A. E. Hoffman and W. G. Leavitt, Properties inherited by the lower radical, Portugal. Math. 27 (1968), 63-66
9	D. R. LaTorre, On h-ideals and k-ideals in hemirings, Publ. Math. Debrecen 12 (1965), 219-226
10	F. A. Szasz, Radicals of Rings, Mathematical Institute Hungarian Academy of Sciences, 1981
11	R. Wiegandt, Radical and Semisimple Classes of Rings, Queen's Papers in Pure and Applied Mathematics, No. 37. Queen's University, Kingston, Ont., 1974
12	M. Zulfiqar, The sum of two radical classes of hemirings, Kyungpook Math. J. 43 (2003), no. 3, 371-374
13	S. M. Yusuf and M. Shabir, Radical classes and semisimple classes for hemirings, Studia Sci. Math. Hungar. 23 (1988), no. 1-2, 231-235