AbstractA 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
AbstractNecessary and sufficient conditions are given for a commutative ring R to be a ring over whi...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
AbstractA sufficient condition is given, involving the grade of an ideal as modified by M. Hochster,...
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b ove...
For the class of matrices over a field, the notion of `rank of a matrix\u27 as defined by `the dimen...
AbstractIn 1952, W.E. Roth showed that matrix equations of the forms AX−YB = C and AX−XB = C over fi...
AbstractWe consider the computational complexity of some problems dealing with matrix rank. Let E, S...
Introduction: It is well known that many of the results in classical linear algebra have an unequivo...
The problem of solving linear equations in a non-commutative algebra is in general a highly non-triv...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
summary:From the fact that the unique solution of a homogeneous linear algebraic system is the trivi...
AbstractLet L be a linear map on the space of n by n matrices with entries in an algebraically close...
AbstractRoth's theorem on the solvability of matrix equations of the form AX−YB=C is proved for matr...
AbstractThe zero-term rank of a matrix is the maximum number of zeros in any generalized diagonal. T...
AbstractNecessary and sufficient conditions are given for a commutative ring R to be a ring over whi...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
AbstractA sufficient condition is given, involving the grade of an ideal as modified by M. Hochster,...
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b ove...
For the class of matrices over a field, the notion of `rank of a matrix\u27 as defined by `the dimen...
AbstractIn 1952, W.E. Roth showed that matrix equations of the forms AX−YB = C and AX−XB = C over fi...
AbstractWe consider the computational complexity of some problems dealing with matrix rank. Let E, S...
Introduction: It is well known that many of the results in classical linear algebra have an unequivo...
The problem of solving linear equations in a non-commutative algebra is in general a highly non-triv...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
summary:From the fact that the unique solution of a homogeneous linear algebraic system is the trivi...
AbstractLet L be a linear map on the space of n by n matrices with entries in an algebraically close...
AbstractRoth's theorem on the solvability of matrix equations of the form AX−YB=C is proved for matr...
AbstractThe zero-term rank of a matrix is the maximum number of zeros in any generalized diagonal. T...
AbstractNecessary and sufficient conditions are given for a commutative ring R to be a ring over whi...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
We prove the following theorem. THEOREM 1. Let D be any commutative principal ideal ring without di...
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