Shahrood University of Technology Journal of Algebraic Systems 2345-5128 10 1 2022 09 01 VALUED-POTENT (GENERAL) MULTIRINGS 49 68 2321 10.22044/jas.2021.10499.1517 EN M. Hamidi Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. 0000-0002-8686-6942 A. A. Tavakoli Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395- 4697, Tehran, Iran. R. Ameri School of Mathematics, Statistics and Computer Sciences, University of Tehran, P.O. Box 14155-6455, Tehran, Iran. Journal Article 2021 01 24 Abstract. This paper extends multirings to a novel concept as general multirings, investigates their properties and presents a special general multirings as notation of (m; n)-potent general multirings. This study analyzes the differences between class of multirings, general multirings and general hyperrings and constructs the class of (in)finite general multirings based on any given non-empty set. In final, we define the concept of hyperideals in general multirings and compare with hyperideals in other<br />similar (hyper)structures. https://jas.shahroodut.ac.ir/article_2321_67c9024c4327e1ad25c24085bc609cb9.pdf