On T-nilpotence of a matrix set
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 36-40.

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Let R be a ring and I be an arbitrary right T-nilpotent subset of R. In the paper it is proved that in this case the set of all n×n-matrices with entries in I is a right T-nilpotent subset of the ring of n×n-matrices with entries in R, where nN. It is also showed that it is impossible to generalize this result for rings of matrices of infinite dimension.
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Yu. P. Maturin. On $T$-nilpotence of a matrix set. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 36-40. https://geodesic-test.mathdoc.fr/item/BASM_2023_2_a3/

[1] Anderson F. W., Fuller K. R., Rings and Categories of Modules, Springer-Verlag, Berlin-Heidelberg-New York, 1992 | MR | Zbl

[2] Faith C., Algebra: Rings, Modules and Categories I, Springer-Verlag, Berlin-Heidelberg-New York, 1973 | MR | Zbl

[3] Horbachuk O. L., “Commutative rings over which all torsions split”, Matematiceskie issledovanija, 24 (1972), 81–90 (in Russian) | MR

[4] Horbachuk O. L., Maturin Yu. P., “Rings and properties of lattices of I-radicals”, Bull. Moldavian Academy of Sci., Math., 1(38) (2002), 44–52 | MR | Zbl

[5] Kasch F., Modules and Rings, Academic Press Inc., London, 1982 | MR | Zbl

[6] Kashu A. I., Radicals and Torsions in Modules, Stiinca, Chisinau, 1983 (in Russian) | MR

[7] Komarnytskyi M. Ya., “Duo-rings over which all torsions are S-torsions”, Matematiceskie issledovanija, 48 (1978), 65–68 (in Russian) | Zbl

[8] Stenstrom Bo., Rings of Quotients. Introduction to Methods of Ring Theory, Springer-Verlag, Berlin-Heidelberg-New York, 1975 | MR | Zbl