Some results on the square-difference factor absorbing hyperideals of a commutative hyperring

Dehghanizadeh, Mohammad Ali

doi:10.22080/cjms.2026.30789.1788

Some results on the square-difference factor absorbing hyperideals of a commutative hyperring

Document Type : Research Articles

Author

Mohammad Ali Dehghanizadeh

Department of Basic Sciences, Technical and Vocational University(TVU), tehran, Iran

10.22080/cjms.2026.30789.1788

Abstract

In this paper, we investigate structural properties of commuta-
tive von Neumann regular hyperrings with a particular emphasis
on the behavior of sdf-absorbing hyperideals. We establish neces-
sary and sufficient conditions under which every proper hyperideal
of such a hyperring is sdf-absorbing. Specifically, we prove that
for a commutative von Neumann regular hyperring R satisfying
0 6= 2 ∈ Z(R), the following statements are equivalent: (a) every
proper hyperideal of R is sdf-absorbing; (b) every nonzero proper
hyperideal of R is sdf-absorbing; and (c) exactly one maximal hy-
perideal M of R has char(R/M) 6= 2. This characterization links
the absorbing behavior of hyperideals with the arithmetic of quo-
tient hyperrings, thereby providing a structural criterion for the
distribution of maximal hyperideals in R.

Keywords