Embedding sums of cancellative modes into functorial sums of affine spaces (Q2772747)

An algebra is said to be entropic if each basis operation is a homomorphism, and a mode is an algebra which is both entropic and idempotent. Subreducts of affine spaces are an important example of modes, and those which are cancellative are of particular interest. This paper investigates the relationship between cancellative modes and affine spaces. The first important result is that each cancellative mode embeds as a subreduct into an affine space. This is then extended to certain sums of modes, and it is shown that any Lallement sum of cancellative modes embeds as a subreduct into a functorial sum of affine spaces. The paper contains many interesting examples.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00067].