Title: Orthogonal complements and extending orthogonal subsets of semimodules
Abstract: In this paper, we first investigate some properties of an orthogonal complement of a subsemimodule and give some necessary and sufficient conditions for every subsemimodule to be equal to the orthogonal complement of its orthogonal complement. Then we obtain some necessary and sufficient conditions for a set of standard orthogonal vectors to be extended to a standard orthogonal basis of a semimodule. As applications, we present two equivalent descriptions for a semiring to be an exact ring by using terminologies of the orthogonal complements and extending orthogonal subsets of semimodules, respectively.
Publication Year: 2021
Publication Date: 2021-07-20
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 1
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