On Hereditary-Like Radicals

Halina France-Jackson

Abstract


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.

Keywords


like-ideal, hereditary-like class, lower radical

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References


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

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