On the dualities between categories of k-completely regular modules |
| |
Authors: | Luca Preciso |
| |
Institution: | Dipartimento di Matematica Pura ed Applicata , Universit` di Padova , via Belzoni 7, Padova, I-35100, Italy |
| |
Abstract: | A semigroup S is called collapsing if there exists a positive integer n such that for every subset of n elements in S at least two distinct words of length n on these letters are equal in S. Let U(A) denote the group of units of an associative algebra A over an infinite field of characteristic p > 0. We show that if A is unitally generated by its nilpotent elements then the following conditions are equivalent: U(A) is collapsing; U(A) satisfies some semigroup identity; U(A) satisfies an Engel identity; A satisfies an Engel identity when viewed as a Lie algebra; and, A satisfies a Morse identity. The characteristic zero analogue of this result was proved by the author in a previous paper. |
| |
Keywords: | |
|
|