TY - JOUR
ID - 103881
TI - On C-injective generalized hyper S-acts
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Ghasempour, Maedeh
AU - Rasouli, Hamid
AU - Iranmanesh, Ali
AU - Barzegar, Hasan
AU - Tehranian, Abolfazl
AD - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
AD - Department of Mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
AD - Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
AD - Department of Mathematics, Tafresh University, Tafresh 39518-
79611, Iran
Y1 - 2023
PY - 2023
VL - 19
IS - 1
SP - 127
EP - 141
KW - hypermonoid
KW - generalized hyper S-act
KW - Injectivity
KW - C-injectivity
KW - semi-injectivity
DO - 10.48308/cgasa.19.1.127
N2 - This paper explores generalized hyper S-acts (GHS-acts) over a hypermonoid S as generalizations of monoid acts within the context of algebraic hyperstructures. Specifically, we extend the definition of C-injectivity to GHS-acts and investigate their internal and homological properties. It is established that for being GHS-injectivity of GHS-acts with a fixed element, it suffices to consider allinclusions from cyclic GHS-subacts into indecomposable ones. Then we introducenew concepts known as semi-injectivity and semi-C-injectivity. By providing examples, we demonstrate that injectivity and semi-injectivity (C-injectivity and semiC-injectivity) are different concepts for GHS-acts, whereas they are the same in the context of acts over monoids. It is also shown that all pure GHS-acts are injective if and only if all pure cyclic GHS-acts are C-injective. Furthermore, we establish an equivalent condition on a hypermonoid S such that all quotients of SS exhibit semi-injectivity. Finally, we derive an equivalent condition for a hypermonoid to beclassified as semi-injective.
UR - https://cgasa.sbu.ac.ir/article_103881.html
L1 - https://cgasa.sbu.ac.ir/article_103881_92769525788a374436c796f5305133ba.pdf
ER -