Publications in Scientific Journals:
M. Pinsker, M. Gehrke:
"Uniform Birkhoff";
Journal of Pure and Applied Algebra,
222
(2018),
5;
1242
- 1250.
English abstract:
We show that pseudovarieties of finitely generated algebras, i.e., classes C of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure UC on the free algebra for C : the members of C then are precisely those finitely generated algebras A for which the natural mapping from the free algebra onto the term clone of A is well-defined and uniformly continuous with respect to the uniformity UC and the uniformity of pointwise convergence on the term clone of A , respectively. Our result unifies earlier theorems describing pseudovarieties of finite algebras and the pseudovariety generated by a single oligomorphic algebra.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.jpaa.2017.06.016
Created from the Publication Database of the Vienna University of Technology.