We find conditions which ensure that a ring is adjoint regular provided that it is a sum of a radical subring with an adjoint regular subring. We also provide a criterion of adjoint regularity for a ring which is a sum of its radical and a regular subring.
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V. A. Andranukievich and Yu. M. Ryabukhin, Radicals of Algebras and Structure Theory [in Russian], Nauka, Moscow (1979).
W. E. Clark, “Generalized radical rings,” Canad. J. Math., 20, No.1, 88–94 (1968).
Du Xiankun, “The structure of generalized radical rings,” Northeastern Math. J., 4, No.1, 101–114 (1988).
Du Xiankun, “The rings with regular adjoint semigroups,” Northeastern Math. J., 4, No.4, 483–488 (1988).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 71–75, 2003.
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Volkov, M.V., Tanana, G.V. On Sums of Radical and Regular Rings. J Math Sci 128, 3378–3380 (2005). https://doi.org/10.1007/s10958-005-0275-z
- Regular Ring