Auslander-Reiten conjecture and finite injective dimension of Hom

Ghosh, Dipankar; Takahashi, Ryo

doi:10.48550/arxiv.2109.00692

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Then depth(ann Remark 4.6. In [18], a few criteria are provided for a module to be free and for a local ring to be Gorenstein in terms of vanishing of certain Ext and injective dimension of Hom. Along with some partial positive answers, a question was raised in [18, Ques.…”

Section: When Ext Modules Have Finite Injective Dimensionmentioning

confidence: 99%

Bibliometric Investigation on Research Productivity in Physics, Chemistry and Mathematics in the Indian Institute of Technology (IIT) Kharagpur during 2001-2020

Ghosh

2021

IJISS

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The study attempts to initiate a bibliometric investigation on the publication trend of research articles of the Indian Institute of Technology(IIT) Kharagpur, the first of the IITs in India recognized as an Institute of National Importance and continued to play a vital role in extending quality education as well as pioneering innovative research in science and engineering. As per the data extracted from SCOPUS on 10.03.2021, IIT Kharagpur contributed 32892 research publications out of which 14130 research publications found in Physics, Chemistry and Mathematics (PCM) in the form of journal articles (11919) and conference paper (2211). The study intends to measure and analyze quantitatively the research productivity of IIT Kharagpur in basic subjects of science, i.e. Physics, Chemistry and Mathematics (PCM) on the basis of the research articles indexed in SCOPUS during last 20 years (2001-2020) with annual growth rate of publications, citations, h-index, authorship pattern, degree of collaboration and other relevant issues. The study also focused on top 15 most prolific authors in terms of productivity count as well as top most favoured sources of publication.

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Section: When Ext Modules Have Finite Injective Dimensionmentioning

confidence: 99%

Bibliometric Investigation on Research Productivity in Physics, Chemistry and Mathematics in the Indian Institute of Technology (IIT) Kharagpur during 2001-2020

Ghosh

2021

IJISS

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“…The Auslander-Reiten conjecture is known to hold true in many particular cases. See [21,Cor. 1.3] and the preceding paragraph for a short survey on this conjecture.…”

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confidence: 99%

Complexity and rigidity of Ulrich modules, and some applications

Dey¹,

Ghosh²

2022

Preprint

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We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can be used as test modules, which detect finite homological dimensions of modules. We prove that Ulrich modules over CM local rings have maximal complexity and curvature. Various new characterizations of local rings are provided in terms of Ulrich modules. We show that every Ulrich module of dimension s over a local ring is (s + 1)-Tor-rigid-test, but not s-Tor-rigid in general (where s 1). Over a deformation of a CM local ring of minimal multiplicity, we also study Tor rigidity.

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Auslander-Reiten conjecture and finite injective dimension of Hom

Cited by 2 publications

References 22 publications

Bibliometric Investigation on Research Productivity in Physics, Chemistry and Mathematics in the Indian Institute of Technology (IIT) Kharagpur during 2001-2020

Bibliometric Investigation on Research Productivity in Physics, Chemistry and Mathematics in the Indian Institute of Technology (IIT) Kharagpur during 2001-2020

Complexity and rigidity of Ulrich modules, and some applications

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