On Hereditary-Like Radicals

Halina France-Jackson


We introduce the concept of like-hereditariness for a class of rings which is a generalization of many important types of hwereditariness. We show that every class of rings is contained in a smallest homomorphically closed like-hereditary class of rings and the lower radical generated by a homomorphically closed like-hereditary class of rings is like-hereditary. This beautifully consolidates all the various "hereditariness" of the lower radical.


like-ideal, hereditary-like class, lower radical

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V. A. Andrunakievich and Yu. M. Ryabukhin, Radicals of algebra and structure theory, Nauka, Moscow, 1979 (in Russian).

Gardner and R. Wiegandt, Radical theory of rings, Marcel Dekker Inc., New York, 2004.

A. E. Hoffman and W. G. Leavitt, Properties inherited by the lower radical, Portugal Math. 27 (1968), 63-66.

R. F. Rossa, More properties inherited by the lower radical, Proc. Amer. Math. Soc. 33 (1972), 247-249.

R. F. Rossa and R. Tangeman, General heredity for radical theory, Proc. Edinburgh Math. Soc. 20 (1976-77), 333-337.

Yu. M. Ryabukhin, Radicals in categories, Mat. Issled. Kishinev 2 (1967), No. 3, 107-165. (in Russian).

A. Sulinski, T. Anderson and N. Divinsky, Lower radical properties for associative and alternative rings, J. London Math. Soc. 41 (1966), 417-424.

R. Tangeman and D. Kreiling, Lower radicals in nonassociative rings, J. Austral. Math. Soc. 14 (1972), 419-423.

J. F. Watters, Lower radicals in associative rings, Canad. J. Math. 21 (1969), 466-476.

DOI: http://dx.doi.org/10.21535%2Fjmsa.v1i1.178


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