Beck modules and alternative algebras. (arXiv:2309.07962v1 [math.RA]) http://arxiv.org/abs/2309.07962
We set out the general theory of "Beck modules" in a variety of algebras and describe them as modules over suitable "universal enveloping" unital associative algebras. We pay particular attention to the somewhat nonstandard case of "alternative algebras," defined by a restricted associative law, and determine the Poincaré polynomial of the universal enveloping algebra in the homogenous case.
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