%0 Journal Article
%T Ideals in pseudo-hoop algebras
%J Journal of Algebraic Hyperstructures and Logical Algebras
%I Hatef College University
%Z 2676-6000
%A Xie, Fei
%A Liu, Hongxing
%D 2020
%\ 11/01/2020
%V 1
%N 4
%P 39-53
%! Ideals in pseudo-hoop algebras
%K Pseudo-hoop algebra
%K ideal
%K congruence
%K Filter
%R 10.52547/HATEF.JAHLA.1.4.3
%X Pseudo-hoop algebras are non-commutative generalizations of hoop-algebras, originally introduced by Bosbach. In this paper, we study ideals in pseudo-hoop algebras. We define congruences induced by ideals and construct the quotient structure. We show that there is a one-toone correspondence between the set of all normal ideals of a pseudo-hoop algebra A with condition (pDN) and the set of all congruences on A. Also, we prove that if A is a good pseudo-hoop algebra with pre-linear condition, then a normal ideal P of A is prime if and only if A/P is a pseudo-hoop chain. Furthermore, we analyse the relationship between ideals and filters of A.
%U http://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf