MMN-2601

# A note on radicals of associative rings and alternative rings

• S. Tumurbat, Department of Mathematics, National University of Mongolia, Ikh Surguuliin Gudamj-1, Ulaanbaatar, Mongolia and, School of Applied Science, Mongolian University of Science and Technology, P.O.Box 75, Ulaanbaatar, Mongolia, stumurbat@hotmail.com
• T. Khulan, National University of Mongolia, Department of Mathematics, Ikh Surguuliin Gudamj-1, Ulaanbaatar, Mongolia, P.O.Box-46A/523, 210646, hulangaaa@yahoo.com
• D. Dayantsolmon, National University of Mongolia, Department of Mathematics, Ikh Surguuliin Gudamj-1, Ulaanbaatar, Mongolia, P.O.Box-46A/523, 210646, dayantsolmon@num.edu.mn

## Abstract

Let $U$ be a universal subclass of a universal class $V$ of rings. We investigate connections of radicals in $U$ and $V$. In \cite{T} we defined $T$ and $T_s$. Let $\gamma \in \{ T, T_s \}$ and let $A$ be a commutative ring with minimum condition on ideals. We give a sufficient and necessary condition when $A$ is $\gamma$-semisimple.

Vol. 23 (2022), No. 1, pp. 175-182
DOI: 10.18514/MMN.2022.2601