Taiwanese Journal of Mathematics

Sequential Purity and Injectivity of Acts over Some Classes of Semigroups

Mojgan Mahmoudi and Gh. Moghaddasi

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The notion of sequential purity for acts over the monoid $\mathbb{N}^\infty$, called projection algebras, was introduced and studied by Mahmoudi and Ebrahimi. This paper is devoted to the study of this notion and its relation to injectivity of $S$-acts for a semigroup $S$. We prove that in general injectivity implies absolute sequential purity and they are equivalent for acts over some classes of semigroups.

Article information

Taiwanese J. Math., Volume 15, Number 2 (2011), 737-744.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 08A60: Unary algebras 08B30: Injectives, projectives 08C05: Categories of algebras [See also 18C05] 20M30: Representation of semigroups; actions of semigroups on sets

sequential pure injective $S$-injective


Mahmoudi, Mojgan; Moghaddasi, Gh. Sequential Purity and Injectivity of Acts over Some Classes of Semigroups. Taiwanese J. Math. 15 (2011), no. 2, 737--744. doi:10.11650/twjm/1500406232. https://projecteuclid.org/euclid.twjm/1500406232

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