Linear equations over commutative rings |
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Authors: | Wai-Sin Ching |
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Institution: | Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210 USA |
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Abstract: | A generalized rank (McCoy rank) of a matrix with entries in a commutative ring R with identity is discussed. Some necessary and sufficient conditions for the solvability of the linear equation Ax = b are derived, where x, b are vectors and A is a matrix with entries in either a Noetherian full quotient ring or a zero dimensional ring. |
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