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math.RA2021
Similarity for zero-square matrices
Grigore Calugareanu
Let T be an n by n zero-square matrix over a commutative unital ring R. We show that T is similar to a multiple of E_1n if R is a GCD domain and n = 2, if R is a GCD domain with 2…
math.RA2021
On unit stable range one matrices
Grigore Calugareanu
We characterize the unit stable range one 2x2 and 3x3 matrices over commutative rings. In particular, we characterize the 2x2 matrices which satisfy the Goodearl-Menal condition. F…
math.RA2021
On idempotent stable range one matrices
Grigore Calugareanu, Horia F. Pop
We characterize the idempotent stable range one matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and e…