NILPOTENCY,SOLVABILITY AND RADICALS IN CATEGORIES |
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Abstract: | Abstract Nilpotent and solvable ideals are defined and investigated in categories. The relation between the prime radical and the sum of the solvable ideals (which is also a radical) is discussed in categories. For example: If an object satisfies the maximal condition for ideals, then the prime radical is equal to the sum of the solvable ideals. Certain generalizations of theorems in rings, groups, Lie algebras, etc. are also proven, for example: An ideal α: I → A is semiprime if and only if A/I contains no non-zero nilpotent ideals. |
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Keywords: | Primary 18D35 Secondary 16A21 17B30 20F14 20F16 20F18 |
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