1 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
| 2 Department of Systems Engineering-Automatic and Informatics Applied, Technical University of Civil Engineering, Bucharest, Romania and International Theoretical High School of Informatics Bucharest, 648, Colentina st., 021187 Bucharest, Romania
In this article, we study ideals in residuated lattice and present a characterization theorem for them. We investigate some related results between the obstinate ideals and other types of ideals of a residuated lattice, likeness Boolean, primary, prime, implicative, maximal and ʘ-prime ideals. Characterization theorems and extension property for obstinate ideal are stated and proved. For the class of ʘ-residuated lattices, by using the ʘ-prime ideals we propose a characterization, and prove that an ideal is an ʘ-prime ideal iff its quotient algebra is an ʘ-residuated lattice. Finally, by using ideals, the class of Noetherian (Artinian) residuated lattices is introduced and Cohen’s theorem is proved.
A. Borumand Saeid and M. Pourkhatoun. Obstinate filters in residuated lattices. Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, 55(4):413–422, 2012.
A. Borumand Saeid and M. Pourkhatoun. Obstinate filters in residuated lattices. Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, 55(4):413–422, 2012.)| false