Abstract
We consider various conditions of the sets of zero-dimensional, Artinian, and von Neumann regular subrings of a commutative ring. Section 1 treats questions of existence of such rings, Section 2 deals with the situation in which all subrings belong to one of the three classes, and Section 3 is concerned with the behavior of the sets under intersection. In Section 4 we give a brief survey of some generalizations and extensions of results of Sections 1–3, as well as some related results.
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Gilmer, R. (1995). Zero-Dimensional Subrings of Commutative Rings. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_16
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DOI: https://doi.org/10.1007/978-94-011-0443-2_16
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