المستخلص: |
Let R be a commutative semiring with identity and M be a unitary R-semimodule. Let N be a proper subsemimodule of M. We say that N is 2-absorbing subsemimodule of M if abm ∈ N where a, b ∈ R and m ∈ M implies that ab ∈ (N: M) or am ∈ N or bm ∈ N. This concept was introduced by M. Dubey and P. Sarohe (see [18]). In this thesis we prove a number of results concerning 2-absorbing subsemimodules. And we generalize the concept of 2-absorbing subsemimodules to weakly 2-absorbing subsemimodules. We also investigate the relation between some subsemimodules and 2-absorbing, weakly 2-absorbing subsemimodules. And we introduce the concepts of 2-absorbing compactly packed semirings and 2-absorbing compactly packed semimodules.
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