THEOREMS RELATED TO IDEALS OF AN L-RING

Gunjan Bansal

Volume 1, Issue 1 2017

Page: 10-23

Abstract

In this paper, we develop a systematic theory for the ideals of an L-ring L(, R) . We introduce the concepts of prime ideal, semiprime ideal, primary ideal and radical of an ideal in an L-ring. We prove several results pertaining to these notions which are versions of their counter part in classical ring theory. Besides this we prove that for a commutative ring R, the radical of a primary ideal  of an L-ring L(,R) is a prime ideal of  provided  has sup-property. Moreover we introduce the concepts of minimal prime ideal and that of irreducibility of an ideal. Furthermore, we introduce the concept of semiprime radical of ideal in an L-ring. Among various results pertaining to this concept, we prove here that semiprime radicals of an ideal  , its radical , and its semiprime radical S() , all coincide.

Back Download



References

  • Mordeson, J.N. and Malik, D.S., Fuzzy Commutative Algebra, World Scientific Publishing Co. USA. 1998.
  • Prajapati, A.S. and Ajmal, N., Maximal ideals of L-subring. --- Communicated.
  • Prajapati, A.S. and Ajmal, N., Maximal ideals of L-subringII. --- Communicated.
  • Prajapati, A.S. and Ajmal, N., Prime ideal, Semiprime ideal and Primary ideal of an L-subring. ---Communicated.
  • Szasz, G. Introduction to Lattice Theory, Academic Press, New York and London, 1963.
  • Yu Yandong, Mordeson, J. N. and Cheng, Shih-Chuan, Elements of L-algebra, Lecture notes in Fuzzy Mathematics and Computer Science 1, Center for Research in Fuzzy Mathematics and Computer Science, Creighton University, USA. 1994.

Looking for Paper Publication??

Come to us.

Submit your Paper