In this article, we define classical prime right ideals of semigroups and generalize them to classical prime subacts of acts. We study the notion of Μ-injectivity where Μ is the class of all classical prime monomorphisms. We investigate the Skornjakov criterion with respect to classical prime injectivity of acts. We characterize their behavior under well-known constructions such as the product, coproduct and direct sum. Among other results, it is proved that an S-act is classical prime injective if and only if it is a classical prime-absolute retract, if and only if it has no classical prime-essential extension.
Sarvghad,N. and Moghaddasi,G. (2025). Classical prime injective S-acts. Journal of Frame and Matrix Theory, 2(2), 6-21. doi: 10.22034/jfmt.2025.508947.1025
MLA
Sarvghad,N. , and Moghaddasi,G. . "Classical prime injective S-acts", Journal of Frame and Matrix Theory, 2, 2, 2025, 6-21. doi: 10.22034/jfmt.2025.508947.1025
HARVARD
Sarvghad N., Moghaddasi G. (2025). 'Classical prime injective S-acts', Journal of Frame and Matrix Theory, 2(2), pp. 6-21. doi: 10.22034/jfmt.2025.508947.1025
CHICAGO
N. Sarvghad and G. Moghaddasi, "Classical prime injective S-acts," Journal of Frame and Matrix Theory, 2 2 (2025): 6-21, doi: 10.22034/jfmt.2025.508947.1025
VANCOUVER
Sarvghad N., Moghaddasi G. Classical prime injective S-acts. JFMT, 2025; 2(2): 6-21. doi: 10.22034/jfmt.2025.508947.1025
