1. CMB 2004 (vol 47 pp. 343)
|Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras |
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.
Keywords:locally nilpotent rings,, nil rings, locally nilpotent semigroups,, semigroup algebras, monomial algebras, infinite words
Categories:16N40, 16S15, 20M05, 20M25, 68R15
2. CMB 1998 (vol 41 pp. 79)
|An answer to a question of Kegel on sums of rings |
We construct a ring $R$ which is a sum of two subrings $A$ and $B$ such that the Levitzki radical of $R$ does not contain any of the hyperannihilators of $A$ and $B$. This answers an open question asked by Kegel in 1964.