TY - JOUR
ID - 135004
TI - Minimal prime ideals in hoops
JO - Journal of Algebraic Hyperstructures and Logical Algebras
JA - JAHLA
LA - en
SN - 2676-6000
AU - Borzooei, R.A.
AU - Aaly, Mona
AD - Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University
AD - Hatef University
Y1 - 2021
PY - 2021
VL - 2
IS - 3
SP - 109
EP - 120
KW - Hoop
KW - ideal
KW - Prime ideal
KW - minimal prime
KW - annihilator
KW - zero divisors
DO - 10.52547/HATEF.JAHLA.2.3.9
N2 - In this paper, we define the notion of minimal prime ideals of hoops and investigate some properties of them. Then by using the notion of annihilators, we study the relation between minimal prime ideals and annihilators. Also, we introduce the notion of zero divisors elements of hoops and prove that the set of all zero divisors of hoops is a union of all minimal prime ideals of hoop. Finally, by using the notions of minimal prime ideals and maximal ideals of hoop, we introduce two new ideals as p-ideal and m-ideal. Then we study some properties of them and investigate the relation between them and prove that every p-ideal of semi-simple hoop is an m-ideal of it.
UR - http://jahla.hatef.ac.ir/article_135004.html
L1 - http://jahla.hatef.ac.ir/article_135004_aa920b87fb4cf022e22d7925e1c2d091.pdf
ER -