Categories and General Algebraic Structures with Applications

Categories and General Algebraic Structures with Applications

$(u,v)$-Absorbing primary hyperideals in multiplicative hyperrings

Articles in Press

Document Type : Research Paper

Author
Mahdi Anbarloei
Faculty of Sciences , Department of Mathematics, Imam Khomeini International University, Qazvin, Iran.
10.48308/cgasa.2026.242779.1589
Abstract
The present paper addresses the notion of $(u,v)$-absorbing primary hyperideals in commutative multiplicative hyperrings. A proper hyperideal $P$ of $A$ is said to be a $(u,v)$-absorbing primary hyperideal if $x_1 \circ \cdots \circ x_u \subseteq P$ for $x_1,\ldots, x_u \in A \backslash U(A)$ implies either $x_1 \circ \cdots \circ x_v \subseteq P$ or $x_{v+1} \circ \cdots \circ x_u \subseteq rad(P)$. The study investigates the links and characteristics of $(u,v)$-absorbing primary hyperideals, presenting a general framework for realizing their importance in hyperring theory. We give some arguments and examples explaining the relationship between $(u,v)$-absorbing primary hyperideals and other famous classes of hyperideals, such as maximal, prime and primary hyperideals, despite
being vastly different. Morevoer, we analyze how the $(u,v)$-absorbing primary hyperideals behave concerning images and inverse images of hyperring homomorphisms, quotients and localizations.
Keywords
Primary hyperideal
maximal hyperideal
$(u, v)$-absorbing primary hyperideal
Subjects
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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 22 July 2026