Эта публикация цитируется в
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Математическая логика, алгебра и теория чисел
Stability of the class of divisible $S$-acts
A. I. Krasitskaya Far Eastern Federal University, 8, Sukhanova str., Vladivostok, 690090, Russia
Аннотация:
We describe monoids
$S$ such that the theory of the class of all divisible
$S$-acts is stable, superstable or, for commutative monoid,
$\omega$-stable. More precisely, we prove that the theory of the class of all divisible
$S$-acts is stable (superstable) iff
$S$ is a linearly ordered (well ordered) monoid. We also prove that for a commutative monoid
$S$ the theory of the class of all divisible
$S$-acts is
$\omega$-stable iff
$S$ is either an abelian group with at most countable number of subgroups or is finite and has only one proper ideal. Classes of regular, projective and strongly flat
$S$-acts were considered in [1, 2]. Using results from [3] we obtain necessary and sufficient conditions for stability, superstability and
$\omega$-stability of theories of classes of all divisible
$S$-acts.
Ключевые слова:
monoid, divisible
$S$-act, stability, superstability,
$\omega$-stability.
УДК:
510.67,
512.56
MSC: 18D35 Поступила 6 апреля 2019 г., опубликована
27 мая 2020 г.
Язык публикации: английский
DOI:
10.33048/semi.2020.17.050