Abstract
AbstractIt is shown that any ring being a sum of two left T-nilpotent subrings is left T-nilpotent. The paper contains the description of all the semigroups S such that an S-graded ring $$R=\bigoplus _{s\in S}A_s$$
R
=
⨁
s
∈
S
A
s
has the property that the left T-nilpotency of all subrings among the subgroups $$A_s$$
A
s
of the additive group of R implies the left T-nilpotency of R. Furthermore, this result is extended to rings R being S-sums.
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Bokut', L.A.: Imbeddings into simple associative algebra, Algebra i Logika15 (1976), 117-142 (in Russian)
2. Algebra and Logic15 (1976), 73-90 (English translation)
3. Clifford, A.H., Preston, G.B.: The algebraic theory of semigroups. Math. Surveys No. 7.1, Amer. Math. Soc. Providence, Vol. I (1961)
4. Ferrero, M., Puczyłowski, E.R.: On rings which are sums of two subrings. Arch. Math. (Basel) 53(1), 4–10 (1989)
5. Ion, I.D.: Some results of the transfinite nilpotence. Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 28(76), 333–336 (1984)