(Weakly) Square-difference factor absorbing hyperideals
Mahdi Anbarloei
TL;DR
The paper introduces and investigates square-difference factor absorbing hyperideals (sdf-absorbing) and their weakly sdf-absorbing counterparts in commutative multiplicative hyperrings. It builds a foundational framework around hyperideals, radicals, and strong C-hyperideals, and establishes key structural results, including $rad(P)=P$ for nonzero sdf-absorbing $\mathcal{C}$-hyperideals and characterizations linked to characteristic $2$ and regularity. It also explores homomorphism and product behavior, showing, for example, how sdf-absorbing properties transfer under quotients and Cartesian products, and provides conditions under which sdf-absorbing hyperideals become prime. These results yield deeper insight into the lattice of hyperideals and their interactions in hyperring constructions, with implications for the structure theory of hyperrings and their quotients.
Abstract
In this paper, we introduce (weakly) square-difference factor absorbing hyperideals in a multiplicative hyperring