# ON ROTH'S PSEUDO EQUIVALENCE OVER RINGS ∗

@article{Hartwig2007ONRP, title={ON ROTH'S PSEUDO EQUIVALENCE OVER RINGS ∗}, author={Robert E. Hartwig and Pedro Patr{\'i}cio}, journal={Electronic Journal of Linear Algebra}, year={2007}, volume={16}, pages={111-124} }

The pseudo-equivalence of a block lower triangular matrix T =( Tij )o ver ar egular ring and its block diagonal matrix D(T )=( Tii) is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form TiiXYT jj = Uij.

## 4 Citations

### The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings

- Mathematics
- 2012

The method of solving matrix linear equations 𝐴 𝑋 + 𝐵 𝑌 = 𝐶 and 𝐴 𝑋 + 𝑌 𝐵 = 𝐶 over commutative Bezout domains by means of standard form of a pair of matrices with respect to generalized…

### On interdependence between invariant factors of a block-triangular matrix and its diagonal blocks

- Mathematics
- 2011

The interdependence between the invariant factors of a block-triangular matrix and its diagonal blocks is established under some constraints on its canonical diagonal form.

### Constructing and counting regular triangular matrices

- Mathematics
- 2020

Von Neumann regularity within a ring of upper triangular matrices is characterized in terms of how such a matrix and an upper triangular generalized inverse can be constructed. In the case of a fin...

## References

SHOWING 1-10 OF 16 REFERENCES

### Roth’s equivalence problem in unit regular rings

- Mathematics
- 1976

It is shown that for matrices over a unit regular ring [A c] [A 0 ] if and only if there exist solutions X and Y to AX YD = C, thus providing a partial generalization to Roth's theorem.

### Block generalized inverses

- Mathematics
- 1976

The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring R. A technique is developed for computing conditional and reflexive inverses for matrices in R2×2, which is…

### Separative cancellation for projective modules over exchange rings

- Mathematics, Economics
- 1998

A separative ring is one whose finitely generated projective modules satisfy the propertyA⊕A⋟A⊕B⋟B⊕B⇒A⋟B. This condition is shown to provide a key to a number of outstanding cancellation problems for…

### The equations $AX-YB=C$ and $AX-XB=C$ in matrices

- Education
- 1952

A method and apparatus for producing variable size alphanumeric, punctuation and other symbol characters having a constant display density. Each character is defined through a matrix by a combination…