A note on the upper radicals of seminearrings.
DOI:
https://doi.org/10.4067/S0716-09172010000100006Keywords:
Near-semirings, semirings, semifields, semi-anillos, semi-campos, cuasi-semianillo.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.
References
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Hoffman, A. E. and Leavitt, W. G., ”Properties inherited by the Lower Radical”, Port. Math. 27, pp. 63-66, (1968).
Krempa, N. J. and Sulinski, A., ”Strong radical properties of alternative and associative rings”, J. Algebra 17, pp. 369-388, (1971).
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Hoorn, V. G. and Rootselaar, B., ” Fundamental notions in the theory of seminerarings”, Compositio Math. 18, pp. 65-78, (1966).
Wiegandt, R., ”Radical and semisimple classes of rings”, Queens University, Ontarto, Canada, (1974).
Weinert, H. J., ”Seminearrings, seminearfield and their semigrouptheoretical background.”, Semigroup Forum 24, pp. 231-254, (1982).
Weinert, H. J., ”Extensions of seminearrings by semigroups of right quotients”, Lect. Notes Math. 998, pp. 412-486, (1983).
Yusuf, S. M. and Shabir, M., ”Radical classes and semisimple classes for hemiring”, Studia Sci. Math. Hungarica 23, pp. 231-235, (1988).
Zulfiqar, M., ”The sum of two radical classes of hemirings”, Kyungpook Math. J. Vol. 43, pp. 371-374, (2003).
Divinsky, N. J., ”Rings and radicals”, Toronto, (1965).
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).
Hebisch, U. and Weinert, H. J., ”Semirings algebraic theory and applications in computer science”, Vol. 5 (Singapore 1998).
Hoffman, A. E. and Leavitt, W. G., ”Properties inherited by the Lower Radical”, Port. Math. 27, pp. 63-66, (1968).
Krempa, N. J. and Sulinski, A., ”Strong radical properties of alternative and associative rings”, J. Algebra 17, pp. 369-388, (1971).
Leavitt, W. G., ”Lower Radical Constructions’, Rings, Modules and Radicals, Budapest, pp. 319-323, (1973).
Olson, D. M. and Jenksins, T. L., ”Radical Theory for Hemirings”, Jour. of Nat. Sciences and Math., Vol. 23, pp. 23-32, (1983).
Szasz, F. A., ”Radicals of rings”, Mathematical Institute Hungarian Academy of Sciences, (1981).
Tangeman, R. L. and Kreiling, D., ”Lower radicals in non-associative rings”, J. Australian Math. Soc. 14, pp. 419-423, (1972).
Hoorn, V. G. and Rootselaar, B., ” Fundamental notions in the theory of seminerarings”, Compositio Math. 18, pp. 65-78, (1966).
Wiegandt, R., ”Radical and semisimple classes of rings”, Queens University, Ontarto, Canada, (1974).
Weinert, H. J., ”Seminearrings, seminearfield and their semigrouptheoretical background.”, Semigroup Forum 24, pp. 231-254, (1982).
Weinert, H. J., ”Extensions of seminearrings by semigroups of right quotients”, Lect. Notes Math. 998, pp. 412-486, (1983).
Yusuf, S. M. and Shabir, M., ”Radical classes and semisimple classes for hemiring”, Studia Sci. Math. Hungarica 23, pp. 231-235, (1988).
Zulfiqar, M., ”The sum of two radical classes of hemirings”, Kyungpook Math. J. Vol. 43, pp. 371-374, (2003).
Published
2011-01-06
How to Cite
[1]
M. Zulfiqar, “A note on the upper radicals of seminearrings.”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 49-56, Jan. 2011.
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