On $$\alpha $$-prime and weakly $$\alpha $$-prime subsemimodules

Existing studies on $$\alpha $$ -prime and weakly $$\alpha $$ -prime submodules have mainly focused on modules over rings, with limited exploration in the setting of semimodules over semirings. In this paper, we extend the definitions and results of Khumprapussorn (Eur J Pure Appl Math 3:730–739, 2018) to $$\alpha $$ -prime subsemimodules of semimodules over commutative semirings. We establish characterizations of weakly $$\alpha $$ -prime subsemimodules and examine their relationships with $$\alpha $$ -prime subsemimodules in both R-semimodule M and the quotient R-semimodule $$M/N_{(Q)}$$ , where N is a partitioning subsemimodule of M. Our results address gaps in previous research and provide new structural insights into prime-like substructures within semimodules over semirings.