@article {
author = {Xie, Fei and Liu, Hongxing},
title = {Ideals in pseudo-hoop algebras},
journal = {Journal of Algebraic Hyperstructures and Logical Algebras},
volume = {1},
number = {4},
pages = {39-53},
year = {2020},
publisher = {Hatef College University},
issn = {2676-6000},
eissn = {2676-6019},
doi = {10.52547/HATEF.JAHLA.1.4.3},
abstract = {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. },
keywords = {Pseudo-hoop algebra,ideal,congruence,Filter},
url = {http://jahla.hatef.ac.ir/article_115370.html},
eprint = {http://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf}
}