## Locally regular varieties.(English)Zbl 0913.08006

An algebra $$A$$ with $$0$$ is called locally regular if, for any congruece $$\sigma$$ on $$A$$, the kernel $$[0]_\sigma$$ is determined by every class $$[a]_\sigma$$. The author characterizes varieties having any algebra locally regular.

### MSC:

 08B05 Equational logic, Mal’tsev conditions 08A30 Subalgebras, congruence relations

### Keywords:

variety of algebras; congruence; locally regular algebra