TY - JOUR ID - 115370 TI - Ideals in pseudo-hoop algebras JO - Journal of Algebraic Hyperstructures and Logical Algebras JA - JAHLA LA - en SN - 2676-6000 AU - Xie, F. AU - Liu, H. AD - School of Mathematics and Statistics, Shandong Normal University, Jinan, P.R.China AD - School of Mathematics and Statistics, Shandong Normal University, Jinan, P.R.China Y1 - 2020 PY - 2020 VL - 1 IS - 4 SP - 39 EP - 53 KW - Pseudo-hoop algebra KW - ideal KW - congruence KW - Filter DO - 10.52547/HATEF.JAHLA.1.4.3 N2 - 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.  UR - https://jahla.hatef.ac.ir/article_115370.html L1 - https://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf ER -