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.
Mahdou, S. E. (2025). Rings in which every regular ideal is projective. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.27374.1662
MLA
Mahdou, S. E. . "Rings in which every regular ideal is projective", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.27374.1662
HARVARD
Mahdou, S. E. (2025). 'Rings in which every regular ideal is projective', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.27374.1662
CHICAGO
S. E. Mahdou, "Rings in which every regular ideal is projective," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.27374.1662
VANCOUVER
Mahdou, S. E. Rings in which every regular ideal is projective. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.27374.1662
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