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, Fei
AU - Liu, Hongxing
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 - http://jahla.hatef.ac.ir/article_115370.html
L1 - http://jahla.hatef.ac.ir/article_115370_36b84974ee41a35317f4c2e0ae2725eb.pdf
ER -