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Hereditary Properties between a Ring and its Maximal Subrings

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Ukrainian Mathematical Journal Aims and scope

We study the existence of maximal subrings and hereditary properties between a ring and its maximal subrings. Some new techniques for establishing the existence of maximal subrings are presented. It is shown that if R is an integral domain and S is a maximal subring of R, then the relation dim(R) = 1 implies that dim(S) = 1 and vice versa if and only if (S : R) = 0. Thus, it is shown that if S is a maximal subring of a Dedekind domain R integrally closed in R; then S is a Dedekind domain if and only if S is Noetherian and (S : R) = 0. We also give some properties of maximal subrings of one-dimensional valuation domains and zero-dimensional rings. Some other hereditary properties, such as semiprimarity, semisimplicity, and regularity are also studied.

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Authors and Affiliations

  1. Chamran University, Ahvaz, Iran

    A. Azarang & O. A. S. Karamzadeh

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  1. A. Azarang
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  2. O. A. S. Karamzadeh
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  3. A. Namazi
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 883–893, July, 2013.

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Azarang, A., Karamzadeh, O.A.S. & Namazi, A. Hereditary Properties between a Ring and its Maximal Subrings. Ukr Math J 65, 981–994 (2013). https://doi.org/10.1007/s11253-013-0836-0

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  • DOI: https://doi.org/10.1007/s11253-013-0836-0

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