N. Kh. Kasymov, A. S. Morozov, I. A. Khodzhamuratova, “<nobr>$T_1$</nobr>-separable numberings of subdirectly indecomposable algebras”, Algebra Logika, 2021, Volume 60, Number 4,Pages <nobr>400

This article is cited in 9 papers

$T_1$-separable numberings of subdirectly indecomposable algebras

N. Kh. Kasymov^a, A. S. Morozov^b, I. A. Khodzhamuratova^a

^a National University of Uzbekistan named after M. Ulugbek, Tashkent
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We prove the existence of a natural subclass of subdirectly indecomposable algebras all of whose Hausdorff numberings are negative. We also construct a $T_1$-separable nonnegative subdirectly indecomposable algebra with Artin congruence lattice.

Keywords: subdirect indecomposability, Artinianness, Noetherianness, computable and enumerable topologies, topological numbered algebras, translational precompleteness, positivity, negativity, effective separability.

UDC: 510.5

Received: 16.12.2020
Revised: 26.11.2021

DOI: 10.33048/alglog.2021.60.402