Localization of tight closure and modules of finite phantom projective dimension.

Abstract Background Small bowel obstruction is a known and potentially lethal complication after gastric bypass surgery, in both the early and the late postoperative course. Colon or large bowel obstruction, on the other hand, seems to be rare after gastric bypass surgery and thus is not routinely considered. Case presentation We present the case of a 21-year old morbidly obese caucasian patient who underwent laparoscopic Roux-en-Y gastric bypass surgery and developed an early severe transverse colon obstruction due to compression of the transverse colon by the antecolic alimentary limb. Emergency revisional surgery showed a short and tense alimentary limb mesentery and possibly tight closure of Petersen’s space contributing to the compression. Through opening of Petersen’s space and mobilization of alimentary limb mesentery, decompression was achieved, and the patient fully recovered. Conclusions This is a rare case of colon obstruction caused by direct compression of the transverse colon by the antecolic alimentary limb. We propose that a combination of short tense alimentary limb mesentery and perhaps tight closure of Petersen’s space was responsible for the obstruction in this case. Surgeons and treating physicians need to be aware of such rare causes of early postoperative bowel obstruction and take these into consideration when evaluating patients.

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Modules of finite projective dimension and cocovers

Mathematische Annalen ◽

10.1007/bf01445260 ◽

1996 ◽

Vol 306 (1) ◽

pp. 445-457 ◽

Cited By ~ 13

Author(s):

Dieter Happel ◽

Luise Unger

Keyword(s):

Projective Dimension ◽

Finite Projective Dimension

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Projective dimension and Brown-Peterson homology

Topology ◽

10.1016/0040-9383(73)90027-x ◽

1973 ◽

Vol 12 (4) ◽

pp. 327-353 ◽

Cited By ~ 39

Author(s):

David Copeland Johnson ◽

W.Stephen Wilson

Keyword(s):

Projective Dimension

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Cellular actions and groups of finite quasi-projective dimension

Mathematische Zeitschrift ◽

10.1007/bf01214714 ◽

1980 ◽

Vol 170 (1) ◽

pp. 85-90 ◽

Cited By ~ 1

Author(s):

James Howie ◽

Hans Rudolf Schneebeli

Keyword(s):

Projective Dimension

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Homological Dimensions Relative to Special Subcategories

Algebra Colloquium ◽

10.1142/s1005386721000122 ◽

2021 ◽

Vol 28 (01) ◽

pp. 131-142

Author(s):

Weiling Song ◽

Tiwei Zhao ◽

Zhaoyong Huang

Keyword(s):

Abelian Category ◽

Projective Dimension ◽

Homological Dimensions ◽

Category Of Modules ◽

The Right

Let [Formula: see text] be an abelian category, [Formula: see text] an additive, full and self-orthogonal subcategory of [Formula: see text] closed under direct summands, [Formula: see text] the right Gorenstein subcategory of [Formula: see text] relative to [Formula: see text], and [Formula: see text] the left orthogonal class of [Formula: see text]. For an object [Formula: see text] in [Formula: see text], we prove that if [Formula: see text] is in the right 1-orthogonal class of [Formula: see text], then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical; if the [Formula: see text]-projective dimension of [Formula: see text] is finite, then the [Formula: see text]-projective and [Formula: see text]-projective dimensions of [Formula: see text] are identical. We also prove that the supremum of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension and that of the [Formula: see text]-projective dimensions of objects with finite [Formula: see text]-projective dimension coincide. Then we apply these results to the category of modules.

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PROPERLY STRATIFIED ALGEBRAS AND TILTING

Proceedings of the London Mathematical Society ◽

10.1017/s0024611505015431 ◽

2005 ◽

Vol 92 (1) ◽

pp. 29-61 ◽

Cited By ~ 8

Author(s):

ANDERS FRISK ◽

VOLODYMYR MAZORCHUK

Keyword(s):

Projective Dimension ◽

Finitistic Dimension ◽

Tilting Module ◽

Tilting Modules ◽

Category Of Modules ◽

Cotilting Modules ◽

Contravariantly Finite ◽

Properly Stratified Algebras ◽

Stratified Algebra ◽

Generalized Tilting Module

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question of when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of properly stratified algebras for which the characteristic tilting and cotilting modules coincide is closed under taking the Ringel dual. Studying stratified algebras whose Ringel dual is properly stratified, we discover a new Ringel-type duality for such algebras, which we call the two-step duality. This duality arises from the existence of a new (generalized) tilting module for stratified algebras with properly stratified Ringel dual. We show that this new tilting module has a lot of interesting properties; for instance, its projective dimension equals the projectively defined finitistic dimension of the original algebra, it guarantees that the category of modules of finite projective dimension is contravariantly finite, and, finally, it allows one to compute the finitistic dimension of the original algebra in terms of the projective dimension of the characteristic tilting module.

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Projective dimension and regularity of the path ideal of the line graph

Journal of Algebra and Its Applications ◽

10.1142/s0219498818500688 ◽

2018 ◽

Vol 17 (04) ◽

pp. 1850068 ◽

Cited By ~ 3

Author(s):

Guangjun Zhu

Keyword(s):

Line Graph ◽

Quotient Ring ◽

Projective Dimension ◽

Algebraic Properties

By generalizing the notion of the path ideal of a graph, we study some algebraic properties of some path ideals associated to a line graph. We show that the quotient ring of these ideals are always sequentially Cohen–Macaulay and also provide some exact formulas for the projective dimension and the regularity of these ideals. As some consequences, we give some exact formulas for the depth of these ideals.

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