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The -semiprimeness of Rings
Grigore Călugăreanu, Tsiu-Kwen Lee, Jerzy Matczuk
For a nonempty subset of a ring , the ring is called -semiprime if, given , implies . This provides a proper class of semiprime rings. First, we…
The formula ABA=Tr(AB)A for matrices
Grigore Calugareanu
We prove that this formula characterizes the square matrices over commutative rings for which all 2 x 2 minors equal zero.
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…
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…
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…
On stable range one matrices
Grigore Calugareanu, Horia F. Pop
For 2 by 2 matrices over commutative rings, we prove a characterization theorem for left stable range 1 elements, we show that the stable range 1 property is left-right symmetric (…
Strictly invariant submodules
Simion Breaz, Grigore Călugăreanu, Andrey Chekhlov
If is an -module, we study the submodules with the property that is invariant with respect to all monomorphisms . Such submodules are called \t…