scholarly journals On preprojective and preinjective partitions of a Δ-good module category

2005 ◽  
Vol 285 (2) ◽  
pp. 608-622 ◽  
Author(s):  
Ziting Zeng
Keyword(s):  
Module Category ◽  
Good Module

scholarly journals Recollements, comma categories and morphic enhancements

2021 ◽  
pp. 1-25
Author(s):  
Xiao-Wu Chen ◽  
Jue Le
Keyword(s):  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Comma Category ◽  
The Right ◽  
Projective Lines ◽  
Triangle Functor

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\mathcal {T}$ , there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\mathcal {T}$ . Examples related to inflation categories and weighted projective lines are discussed.

A Note on the Radical of a Module Category

2013 ◽  
Vol 41 (12) ◽  
pp. 4419-4424 ◽  
Author(s):  
Claudia Chaio ◽  
Shiping Liu
Keyword(s):  
Module Category

scholarly journals THE GRADED CENTER OF A TRIANGULATED CATEGORY

2016 ◽  
Vol 102 (1) ◽  
pp. 74-95
Author(s):  
JON F. CARLSON ◽  
PETER WEBB
Keyword(s):  
Group Algebra ◽  
Special Kind ◽  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Stable Module Category ◽  
Natural Transformations ◽  
Stable Module ◽  
Serre Functor

With applications in mind to the representations and cohomology of block algebras, we examine elements of the graded center of a triangulated category when the category has a Serre functor. These are natural transformations from the identity functor to powers of the shift functor that commute with the shift functor. We show that such natural transformations that have support in a single shift orbit of indecomposable objects are necessarily of a kind previously constructed by Linckelmann. Under further conditions, when the support is contained in only finitely many shift orbits, sums of transformations of this special kind account for all possibilities. Allowing infinitely many shift orbits in the support, we construct elements of the graded center of the stable module category of a tame group algebra of a kind that cannot occur with wild block algebras. We use functorial methods extensively in the proof, developing some of this theory in the context of triangulated categories.

scholarly journals Cohomology of Modules Over -categories and Co--categories

2019 ◽  
Vol 72 (5) ◽  
pp. 1352-1385
Author(s):  
Mamta Balodi ◽  
Abhishek Banerjee ◽  
Samarpita Ray
Keyword(s):  
Hopf Algebra ◽  
Module Category ◽  
Spectral Sequences ◽  
Locally Finite ◽  
Hopf Module ◽  
Comodule Algebra ◽  
Hopf Modules ◽  
Derived Functors

AbstractLet $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category ${\mathcal{C}}$ as modules over the smash extension ${\mathcal{C}}\#H$. We construct Grothendieck spectral sequences for the cohomologies as well as the $H$-locally finite cohomologies of these objects. We also introduce relative $({\mathcal{D}},H)$-Hopf modules over a Hopf comodule category ${\mathcal{D}}$. These generalize relative $(A,H)$-Hopf modules over an $H$-comodule algebra $A$. We construct Grothendieck spectral sequences for their cohomologies by using their rational $\text{Hom}$ objects and higher derived functors of coinvariants.

Clustering Techniques for Software Engineering

2016 ◽  
Vol 4 (2) ◽  
pp. 465 ◽  
Author(s):  
Shohag Barman ◽  
Hira Lal Gope ◽  
M M Manjurul Islam ◽  
Md Mehedi Hasan ◽  
Umme Salma
Keyword(s):  
Software Engineering ◽  
Research Direction ◽  
Maintenance Cost ◽  
Software Systems ◽  
Module Structure ◽  
Result Section ◽  
Clustering Techniques ◽  
Software Clustering ◽  
Good Module ◽  
Industrial Software

<p>Software industries face a common problem which is the maintenance cost of industrial software systems. There are lots of reasons behind this problem. One of the possible reasons is the high maintenance cost due to lack of knowledge about understanding the software systems that are too large, and complex. Software clustering is an efficient technique to deal with such kind of problems that arise from the sheer size and complexity of large software systems. Day by day the size and complexity of industrial software systems are rapidly increasing. So, it will be a challenging task for managing software systems. Software clustering can be very helpful to understand the larger software system, decompose them into smaller and easy to maintenance. In this paper, we want to give research direction in the area of software clustering in order to develop efficient clustering techniques for software engineering. Besides, we want to describe the most recent clustering techniques and their strength as well as weakness. In addition, we propose genetic algorithm based software modularization clustering method. The result section demonstrated that proposed method can effectively produce good module structure and it outperforms the state of the art methods. </p>

scholarly journals The Tilting–Cotilting Correspondence

2019 ◽  
Author(s):  
Leonid Positselski ◽  
Jan Šťovíček
Keyword(s):  
Abelian Category ◽  
Derived Categories ◽  
Module Category ◽  
Topological Ring ◽  
Projective Generator ◽  
Derived Equivalences ◽  
Wide Range ◽  
Injective Cogenerator ◽  
Tilting Object

Abstract To a big $n$-tilting object in a complete, cocomplete abelian category ${\textsf{A}}$ with an injective cogenerator we assign a big $n$-cotilting object in a complete, cocomplete abelian category ${\textsf{B}}$ with a projective generator and vice versa. Then we construct an equivalence between the (conventional or absolute) derived categories of ${\textsf{A}}$ and ${\textsf{B}}$. Under various assumptions on ${\textsf{A}}$, which cover a wide range of examples (for instance, if ${\textsf{A}}$ is a module category or, more generally, a locally finitely presentable Grothendieck abelian category), we show that ${\textsf{B}}$ is the abelian category of contramodules over a topological ring and that the derived equivalences are realized by a contramodule-valued variant of the usual derived Hom functor.

scholarly journals Recollement of homotopy categories and Cohen-Macaulay modules

2011 ◽  
Vol 8 (3) ◽  
pp. 507-542 ◽  
Author(s):  
Osamu Iyama ◽  
Kiriko Kato ◽  
Jun-ichi Miyachi
Keyword(s):  
Homotopy Category ◽  
Module Category ◽  
Gorenstein Ring ◽  
Projective Modules ◽  
Finitely Generated ◽  
Stable Module Category ◽  
Quotient Category ◽  
Stable Module

AbstractWe study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show the existence of a new structure in the above quotient category, which we call a triangle of recollements. Moreover, we show that this quotient category is triangle equivalent to the stable module category of Cohen-Macaulay T2(R)-modules.

scholarly journals Static Subcategories of the Module Category of a Finite-Dimensional Hereditary Algebra

2016 ◽  
Vol 44 (6) ◽  
pp. 2531-2546
Author(s):  
Mustafa A. A. Obaid ◽  
S. Khalid Nauman ◽  
Wafaa M. Fakieh ◽  
Claus Michael Ringel
Keyword(s):  
Module Category ◽  
Hereditary Algebra ◽  
Finite Dimensional
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