Bases in semilinear spaces over zerosumfree semirings |
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Authors: | Qian-yu Shu |
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Institution: | College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, People’s Republic of China |
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Abstract: | This paper investigates the cardinality of a basis and the characterizations of a basis in semilinear space of n-dimensional vectors over zerosumfree semirings. First, it discusses the cardinality of a basis and gives some necessary and sufficient conditions that each basis has the same number of elements. Then it presents some conditions that a set of vectors is a basis and that a set of linearly independent vectors can be extended to a basis. In the end, it shows a necessary and sufficient condition that two semilinear spaces are isomorphic. |
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Keywords: | 15A03 |
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