Journal
ALGEBRA AND LOGIC
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1007/s10469-023-09718-x
Keywords
monoid; act over monoid; injective act; generalized stability
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The paper focuses on injective S-acts with a P-stable theory and proves that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Additionally, it describes commutative and linearly ordered monoids S for which the class of injective S-acts is (P, s)-, (P, a)-, and (P, e)-stable.
The concept of P-stability is a particular case of generalized stability of complete theories. We study injective S-acts with a P-stable theory. It is proved that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Also we describe commutative and linearly ordered monoids S the class of injective S-acts over which is (P, s)-, (P, a)-, and (P, e)-stable.
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