Strongly prime radical of group algebras.
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The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.
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Various kinds of radicals of ideals in commutative rings with identity appear in many parts of algebra and geometry, in particular in connection with the Hilbert Nullstellensatz, both in the noetherian and the non-noetherian case. All of these radicals, except the *-radicals, have the fundamental, and very useful, property that the radical of an ideal is the intersection of radical primes, that is, primes that are equal to their own radical. It is easy to verify that...
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We show that there exist zero-symmetric simple nearrings with identity, which are not equiprime, solving a longstanding open problem.
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