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math.RA2024
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…
math.RA2023
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.