Hatef College UniversityJournal of Algebraic Hyperstructures and Logical Algebras2676-60001420201101Ideals in pseudo-hoop algebras395311537010.52547/HATEF.JAHLA.1.4.3ENFeiXieSchool of Mathematics and Statistics, Shandong Normal University,
Jinan, P.R.ChinaHongxingLiuSchool of Mathematics and Statistics, Shandong Normal University,
Jinan, P.R.ChinaJournal Article20201003Pseudo-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. http://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf