Kostaq Hila - Department of Mathematical Engineering, Polytechnic University of Tirana, Albania
Elif Kaya - Department of Mathematics and Science Education, Istanbul Sabahattin Zaim University, Istanbul, Turkiye
Melis Bolat - Department of Computer Engineering, Istanbul Gelisim University, Istanbul, Turkiye
Bayram Ersoy - Department of Mathematics, Yildiz Technical University, Istanbul, Turkiye
Serkan Onar - Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkiye
Bijan Davvaz - Department of Mathematics, Yazd University, Yazd, Iran

In this paper, we study commutative Krasner hyperrings with nonzero identity and nonzero unital hypermodules. We introduce a new concept, the \delta-primary subhypermodule on Krasner hyperrings. Some characterizations and properties for \delta-primary subhypermodules using the expansion function \delta are provided. The images and inverse images of \delta-primary subhypermodules under homomorphism are investigated. Finally, some characterizations for multiplication hypermodules with some special conditions are provided.

δ-primary subhypermodules, expansion of subhypermodules, multiplication hypermodules, Krasner hyperring