Structure Theory of Faithful Rings, Iii. Irreducible Rings
نویسنده
چکیده
The first two papers of this series1 were primarily concerned with a closure operation on the lattice of right ideals of a ring and the resulting direct-sum representation of the ring in case the closure operation was atomic. These results generalize the classical structure theory of semisimple rings. The present paper studies the irreducible components encountered in the direct-sum representation of a ring in (F II). For semisimple rings, these components are primitive rings. Thus, primitive rings and also prime rings are special instances of the irreducible rings discussed in this paper.
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