On minimal extensions of rings
نویسنده
چکیده
Given two rings R ⊆ S, S is said to be a minimal ring extension of R if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro, and Ferrand & Olivier on commutative minimal extensions.
منابع مشابه
On derivations and biderivations of trivial extensions and triangular matrix rings
Triangular matrix rings are examples of trivial extensions. In this article we determine the structure of derivations and biderivations of the trivial extensions, and thereby we describe the derivations and biderivations of the upper triangular matrix rings. Some related results are also obtained.
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