A note on the upper radicals of seminearrings.

• Zulfiqar, Muhammad ^[1]
  1. [1] Quaid-i-Azam University

     Quaid-i-Azam University

     Pakistán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 1, 2010, págs. 49-56
• Idioma: inglés
• DOI: 10.4067/S0716-09172010000100006
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas Birkenmeier, G. F., ”Seminearrings and nearrings” induced by the circle operation, preprint, (1989).
  • 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...
  • 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).