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.
Xie, F., Liu, H. (2020). Ideals in pseudo-hoop algebras. Journal of Algebraic Hyperstructures and Logical Algebras, 1(4), 39-53. doi: 10.52547/HATEF.JAHLA.1.4.3
MLA
Fei Xie; Hongxing Liu. "Ideals in pseudo-hoop algebras". Journal of Algebraic Hyperstructures and Logical Algebras, 1, 4, 2020, 39-53. doi: 10.52547/HATEF.JAHLA.1.4.3
HARVARD
Xie, F., Liu, H. (2020). 'Ideals in pseudo-hoop algebras', Journal of Algebraic Hyperstructures and Logical Algebras, 1(4), pp. 39-53. doi: 10.52547/HATEF.JAHLA.1.4.3
VANCOUVER
Xie, F., Liu, H. Ideals in pseudo-hoop algebras. Journal of Algebraic Hyperstructures and Logical Algebras, 2020; 1(4): 39-53. doi: 10.52547/HATEF.JAHLA.1.4.3
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