arXiv subjects
Publications and source records attributed to A. Kadji.
The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Lukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.
Residuated lattices play an important role in the study of fuzzy logic based of t-norm. In this paper, we introduced the notions of n-fold implicative filters, n-fold positive implicative filters, n-fold boolean filters, n-fold fantastic filters, n-fold normal filters and n-fold obstinate filters in residuated lattices and study the relations among them. This generalized the similar existing results in BL-algebra with the connection of the work of Kerre and all in [14], Kondo and all in [7], [11] and Motamed and all in [9]. At the end of this paper, we draw two diagrams; the first one describe the relations between some type of n-fold filters in residuated lattices and the second one describe the relations between some type of n-fold residuated lattices.