October 2, 2025Open Access

On 1-absorbing prime and weakly 1-absorbing prime subsemimodules

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This paper introduces 1-absorbing prime and weakly 1-absorbing prime subsemimodules, highlighting their properties in commutative semirings.

A subsemimodule is 1-absorbing prime if abm in N implies ab in (N :_{S} M) or m in N.
Weakly 1-absorbing prime subsemimodules require nonzero products of proper ideals to satisfy specific conditions.
The study shows key properties connecting subsemimodules and ideals in a commutative semiring framework.
Characterizations of both prime types link definitions with broader structural implications for semiranges.

Adarbeh et al. (2025) studied this question.

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This paper introduces 1-absorbing prime and weakly 1-absorbing prime subsemimodules, highlighting their properties in commutative semirings.