Rings in which every regular ideal is projective

Document Type : Research Paper

Author

Laboratory of Modelling and Mathematical Structures, Faculty of Science and Technology of Fez, University S. M. Ben Abdellah Fez, Morocco

Abstract

In this paper, we introduce a new class of ring called regular hereditary ring, which is a weak version of hereditary
ring property. Any hereditary ring is naturally a regular hereditary ring, and in the domain context, these two forms coincide to become a Dedekind domain. We study the transfer of this notion to various context of commutative ring extensions such as localization, direct product, trivial ring extensions and pullbacks. Our results generate new families of examples of non-hereditary regular hereditary rings.

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References

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