The quotient category of a Morita context

The main purpose of the paper is to consider two Morita equivalent semirings [Formula: see text] and [Formula: see text] via Morita context [Formula: see text] instead of considering them via the equivalence of the resulting semimodule categories and then to investigate various Morita invariants related to each of the pairs [Formula: see text]; [Formula: see text]; [Formula: see text]; [Formula: see text], etc.

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The completion of a morita context

Communications in Algebra ◽

10.1080/00927878008822487 ◽

1980 ◽

Vol 8 (8) ◽

pp. 717-742 ◽

Cited By ~ 2

Author(s):

John J. Hutchinson

Keyword(s):

Morita Context

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Prime structures in a Morita context

Boletín de la Sociedad Matemática Mexicana ◽

10.1007/s40590-020-00295-y ◽

2020 ◽

Vol 26 (3) ◽

pp. 991-1001

Author(s):

Mete Burak Calci ◽

Sait Halicioglu ◽

Abdullah Harmanci ◽

Burcu Ungor

Keyword(s):

Morita Context

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Decomposing the complexity quotient category

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100001572 ◽

1996 ◽

Vol 120 (4) ◽

pp. 589-595

Author(s):

D. J. Benson

Keyword(s):

Representation Theory ◽

Finite Groups ◽

Modular Representation ◽

Recent Effort ◽

Finitely Generated ◽

Modular Representation Theory ◽

Joint Work ◽

Quotient Category ◽

Finitely Generated Modules

In the modular representation theory of finite groups, much recent effort has gone into describing cohomological properties of the category of finitely generated modules. In recent joint work of the author with Jon Carlson and Jeremy Rickard[3], it has become clear that for some purposes the finiteness restriction is undesirable. In particular, in the quotient category of kG-modules by the subcategory of modules of less than maximal complexity, it turns out that finitely generated modules can have infinitely generated summands, and that including these summands in the category repairs the lack of Krull–Schmidt property.

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Maschke-type theorem and Morita context over weak Hopf algebras

Science in China Series A Mathematics ◽

10.1007/s11425-006-0587-6 ◽

2006 ◽

Vol 49 (5) ◽

pp. 587-598 ◽

Cited By ~ 15

Author(s):

Liangyun Zhang

Keyword(s):

Hopf Algebras ◽

Type Theorem ◽

Morita Context ◽

Maschke Type Theorem ◽

Weak Hopf Algebras

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On a characterization of finitely presented functors

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1989.0109 ◽

1989 ◽

Vol 425 (1869) ◽

pp. 329-339

Keyword(s):

Representation Type ◽

Equivalence Of Categories ◽

Quotient Category ◽

Auslander Algebra ◽

Finitely Presented

The concept of finitely presented functor was introduced by Auslander. Proposition 3.1 of Auslander & Reiten provides a way of dealing with the category of finitely presented functors, that seems concrete and easy to use, at least in some examples. The study of this category, using this particular line of thought, is the main purpose of this work. In §1 I recall some basic definitions and give the required notation. In §2 I state the theorem of Auslander & Reiten referred to above and give a new proof of this result. The first part of this proof is an immediate consequence of the theory developed by Green. In §3 I state and prove an unpublished theorem by J. A. Green and I introduce a new category I such that the category of finitely presented functors. mmod A , is equivalent to a quotient category I / J , where J is an ideal of I . In §4 I give some examples of properties of mmod A , stated and proved in terms of the category I , by using the equivalence of categories referred to in §3. In §5 I consider the particular case where A = A q = k -alg < z : z q = 0>, apply the results of previous sections to study mmod A q and make conclusions about the representation type of the Auslander algebra of A q .

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Characterizations of Morita-like Equivalences for Right XST-Rings

Algebra Colloquium ◽

10.1142/s1005386707000090 ◽

2007 ◽

Vol 14 (01) ◽

pp. 85-95

Author(s):

Baiyu Ouyang ◽

Liren Zhou ◽

Wenting Tong

Keyword(s):

Universal Theory ◽

Morita Context

The notion of xst-rings was introduced by García and Marín in 1999. In this paper, we characterize Morita-like equivalences for right xst-rings, obtain the universal theory of Morita equivalences, and prove that two right xst-rings R and T are Morita-like equivalent if and only if there is a Morita context between R and T. We also prove that Morita-like equivalences can be realized by the covariant functors Hom and ⊗ for these rings.

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Recollement of homotopy categories and Cohen-Macaulay modules

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is011003007jkt143 ◽

2011 ◽

Vol 8 (3) ◽

pp. 507-542 ◽

Cited By ~ 18

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.

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