Duality Pairs Induced by One-Sided Gorenstein Subcategories

Let [Formula: see text] be an integer. We introduce the notions of [Formula: see text]-FP-gr-injective and [Formula: see text]-gr-flat modules. Then we investigate the properties of these modules by using the properties of special finitely presented graded modules and obtain some equivalent characterizations of [Formula: see text]-gr-coherent rings in terms of [Formula: see text]-FP-gr-injective and [Formula: see text]-gr-flat modules. Moreover, we prove that the pairs (gr-[Formula: see text], gr-[Formula: see text]) and (gr-[Formula: see text], gr-[Formula: see text]) are duality pairs over left [Formula: see text]-coherent rings, where gr-[Formula: see text] and gr-[Formula: see text] denote the subcategories of [Formula: see text]-FP-gr-injective left [Formula: see text]-modules and [Formula: see text]-gr-flat right [Formula: see text]-modules respectively. As applications, we obtain that any graded left (respectively, right) [Formula: see text]-module admits an [Formula: see text]-FP-gr-injective (respectively, [Formula: see text]-gr-flat) cover and preenvelope.

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Model structures, recollements and duality pairs

Journal of Algebra and Its Applications ◽

10.1142/s0219498823500172 ◽

2021 ◽

Author(s):

Wenjing Chen ◽

Zhongkui Liu

Keyword(s):

Projective Modules ◽

Cotorsion Pair ◽

Gorenstein Rings ◽

Injective Modules ◽

Flat Modules ◽

Duality Pairs ◽

Cotorsion Pairs ◽

Gorenstein Flat ◽

Model Structures

In this paper, we construct some model structures corresponding Gorenstein [Formula: see text]-modules and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and cotorsion pairs. By investigating homological properties of Gorenstein [Formula: see text]-modules and some known complete hereditary cotorsion pairs, we describe several types of complexes and obtain some characterizations of Iwanaga–Gorenstein rings. Based on some facts given in this paper, we find new duality pairs and show that [Formula: see text] is covering as well as enveloping and [Formula: see text] is preenveloping under certain conditions, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-injective modules and [Formula: see text] denotes the class of Gorenstein [Formula: see text]-flat modules. We give some recollements via projective cotorsion pair [Formula: see text] cogenerated by a set, where [Formula: see text] denotes the class of Gorenstein [Formula: see text]-projective modules. Also, many recollements are immediately displayed through setting specific complete duality pairs.

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Duality Pairs Induced by Gorenstein Projective Modules with Respect to Semidualizing Modules

Algebras and Representation Theory ◽

10.1007/s10468-015-9529-8 ◽

2015 ◽

Vol 18 (4) ◽

pp. 989-1007 ◽

Cited By ~ 1

Author(s):

Jiangsheng Hu ◽

Yuxian Geng ◽

Nanqing Ding

Keyword(s):

Projective Modules ◽

Duality Pairs ◽

Gorenstein Projective Modules ◽

Semidualizing Modules

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Regular families of forests, antichains and duality pairs of relational structures

COMBINATORICA ◽

10.1007/s00493-015-3003-4 ◽

2016 ◽

Vol 37 (4) ◽

pp. 651-672 ◽

Cited By ~ 3

Author(s):

Péter L. Erdős ◽

Dömötör Pálvölgyi ◽

Claude Tardif ◽

Gábor Tardos

Keyword(s):

Relational Structures ◽

Duality Pairs

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Cotorsion pairs induced by duality pairs

Journal of Commutative Algebra ◽

10.1216/jca-2009-1-4-621 ◽

2009 ◽

Vol 1 (4) ◽

pp. 621-633 ◽

Cited By ~ 32

Author(s):

Henrik Holm ◽

Peter Jørgensen

Keyword(s):

Duality Pairs ◽

Cotorsion Pairs

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Motives in creating an LGBTQ inclusive work environment: a case study

Qualitative Research in Organizations and Management An International Journal ◽

10.1108/qrom-09-2019-1822 ◽

2021 ◽

Vol 16 (1) ◽

pp. 237-260

Author(s):

Brent S. Opall

Keyword(s):

Work Environment ◽

Return On Investment ◽

Multiple Case Study ◽

Work Environments ◽

Valuable Insight ◽

Case Study Methodology ◽

Content Type ◽

Duality Pairs ◽

Multiple Case

PurposeThe purpose of this inquiry is to examine why companies create LGBTQ-inclusive work environments and how these firms advance LGBTQ-inclusiveness through CSR practices and address challenges presented by strategic duality.Design/methodology/approachUsing a qualitative multiple case study design, data was collected and then triangulated from interviews and company documents. NVivo, a qualitative research program, was used to organize, sort, query and model the data.FindingsSeveral themes were identified as reasons why Fortune 500 organizations sought to create LGBTQ-inclusive work environments. Themes include a positive return on investment, advancing human rights issues within the framework of corporate social responsibility (CSR), internal organizational pressure and parity with other Minnesota companies. Findings are examined through the theoretical lens of strategic duality.Research limitations/implicationsPrimary theoretical implications include contributions to our understanding of strategic duality by providing a first-hand account from people in organizations that encountered imperatives that to some degree are in conflict. By design, the multiple case study methodology does not allow generalizations to be drawn beyond the organizations included in this study.Practical implicationsBoth managers and researchers will find this study provides valuable insight on how people and organizations experience and navigate strategic duality (pairs of competing imperatives) within the context of the motivation behind creating an LGBTQ-inclusive work environment.Originality/valueThis inquiry provides a unique and valuable account as to why organizations choose to invest resources in creating a LGBTQ-inclusive work environment, the return on investment (ROI) and examines competing imperatives (strategic dualities) faced by management. Similar multiple case studies of this qualitative nature are rare, possibly even non-existent and, therefore, this study makes a significant contribution to the literature.

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