Richard F. Bartels

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20232026

most citedGeneralized Loewy length of Cohen-Macaulay local and graded rings

1 citations · 1 across the 5 of their papers we have counts for

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math.AC2026

Reduction numbers for witnesses to the generalized Loewy length

Richard Bartels, Sarah Dajani, Gabriel Koomson

Let $(R, m)$ be a one-dimensional Cohen-Macaulay local ring. In this paper, we find the reduction number $r_{z} (m^{d})$ of $m^{d}$ with respect to a wit…

math.AC2026

Cohen-Macaulay approximations over generically Gorenstein rings

Richard F. Bartels

Let $(R, m)$ be a Cohen-Macaulay local ring with canonical module that is generically Gorenstein. In this paper, I prove isomorphisms relating the minimal MCM approximati…

math.AC2025

Cohen-Macaulay approximations and the $SC_{r}$ -condition

Richard F. Bartels

We study the relation between MCM approximations and FID hulls of modules over a Cohen-Macaulay local ring $R$ with canonical module, specifically when $R$ is generically Gorenstei…

math.AC2024

Some properties of ideals in Cohen-Macaulay local rings

Richard F. Bartels

For a Cohen-Macaulay local ring $(R, m)$ with canonical module, we study how relations between $index (R)$ and $g ℓℓ (R)$ and between $index (R)$ a…

math.AC2023★ 1 cited

Generalized Loewy length of Cohen-Macaulay local and graded rings

Richard Bartels

We generalize a theorem of Ding relating the generalized Loewy length $g ℓℓ (R)$ and index of a one-dimensional Cohen-Macaulay local ring $(R, m, k)$ . Ding prov…

Reduction numbers for witnesses to the generalized Loewy length

Cohen-Macaulay approximations over generically Gorenstein rings

Cohen-Macaulay approximations and the SCr​-condition

Some properties of ideals in Cohen-Macaulay local rings

Generalized Loewy length of Cohen-Macaulay local and graded rings

Cohen-Macaulay approximations and the $SC_{r}$ -condition