K. A. Kolesnikova, “Artinian and Noetherian polygons over completely <nobr>$0$</nobr>-simple semigroups”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, Number 5,Pages <nobr>67

This article is cited in 2 papers

Short notes

Artinian and Noetherian polygons over completely $0$-simple semigroups

K. A. Kolesnikova^ab

^a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b National Research University of Electronic Technology, Institute of Physics and Applied Mathematics

Abstract: Necessary and sufficient conditions for act over a completely $0$-simple semigroup to be Artinian and Noetherian are obtained. It is demonstrated that the direct product of Artinian and Noetherian acts, generally speaking, is not Artinian and Noetherian.

Key words: act over semigroup, completely simple semigroup, completely $0$ simple semigroup, Artinian, Noetherian, finiteness conditions.

UDC: 512.579

Received: 05.07.2023

DOI: 10.55959/MSU0579-9368-1-65-5-8