Square-Difference Factor Absorbing Primary Hyperideals of Multiplicative Hyperrings
Mathematics, vol.14, no.15, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 15
- Publication Date: 2026
- Doi Number: 10.3390/math14152784
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Cartesian product, hyperideal characterization, localization, multiplicative hyperring, primary hyperideal, sdf-absorbing hyperideal, sdf-absorbing primary hyperideal
- Yıldız Technical University Affiliated: Yes
Abstract
We introduce and study square-difference factor absorbing primary hyperideals (sdf-absorbing primary hyperideals) in commutative multiplicative hyperrings. A proper hyperideal I is called sdf-absorbing primary if (Formula presented.) implies (Formula presented.) or (Formula presented.). This class provides a proper common generalization of both primary hyperideals and sdf-absorbing hyperideals. We establish a comprehensive characterization; investigate the behavior under homomorphisms, localization, intersections, ascending chains, and Cartesian products; and identify the precise conditions under which the three notions coincide.