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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive
Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2023 Volume 219, Pages 60–130 (Mi into1110)
Centrally essential rings and semirings

A. Tuganbaevab

a Lomonosov Moscow State University
b National Research University "Moscow Power Engineering Institute"

Abstract: In this survey, we systematically examine rings and semirings that are either commutative or satisfy the following condition: for any noncentral element $a$, there exist nonzero central elements $x$ and $y$ such that $ax=y$.

Keywords: ring, associative ring, commutative ring, centrally essential ring, group algebra, module, ideal.

UDC: 512.5

MSC: 16R99, 20K30

DOI: 10.36535/0233-6723-2022-219-60-130


© Steklov Math. Inst. of RAS, 2025