The projective limit of the spaces
J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)
Colloquium Mathematicae
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J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)
Colloquium Mathematicae
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Rüdiger Göbel, Saharon Shelah (2006)
Fundamenta Mathematicae
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An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra of the R-module , taking any a ∈ A to the right multiplication by a, is an isomorphism of algebras. In this case is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18,...
A. L. Agore (2010)
Colloquium Mathematicae
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We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if for all . In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.
Christine Vespa (2008)
Fundamenta Mathematicae
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We continue the study of the category of functors , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in : and . As an application of these two decompositions, we give a complete description of the polynomial...
Xiaorui Zhai, Chunxia Zhang (2016)
Czechoslovak Mathematical Journal
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Let be an associative ring with identity and a class of -modules. In this article: we first give a detailed treatment of Cartan-Eilenberg complexes and extend the basic properties of the class to the class ). Secondly, we study and give some equivalent characterizations of Cartan-Eilenberg projective, injective and flat complexes which are similar to projective, injective and flat modules, respectively. As applications, we characterize some classical rings in terms of these...
Xinhong Chen, Ming Lu (2015)
Colloquium Mathematicae
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Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
Shiquan Ruan, Li Wang, Haicheng Zhang (2024)
Czechoslovak Mathematical Journal
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For any positive integer , let be a linearly oriented quiver of type with vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories and , where and are the two extriangulated categories corresponding to the representation category of and the morphism category of projective representations of , respectively. As a...
Josef Vala (1988)
Časopis pro pěstování matematiky
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Eva Ferrara Dentice (2018)
Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
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In the paper (Ferrara Dentice et al., 2004) a complete exposition of the state of the art for lax embeddings of polar spaces of finite rank is presented. As a consequence, we have that if a Grassmann space of dimension 3 and index 1 has a lax embedding in a projective space over a skew–field , then is the Klein quadric defined over a subfield of . In this paper, I examine Grassmann spaces of arbitrary dimension and index having a lax embedding in a projective space.
Zenobia Anusiak (1971)
Colloquium Mathematicae
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Leonid F. Barannyk, Dariusz Klein (2004)
Colloquium Mathematicae
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Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by the set of isomorphism classes of indecomposable -modules of S-rank m. We exhibit rings for which there exists a function such that and is an infinite set for every natural n > 1. In special cases contains every natural...
Zhongwei Wang, Liangyun Zhang (2015)
Colloquium Mathematicae
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Let denote the twisted smash product of an arbitrary algebra A and a Hopf algebra H over a field. We present an analogue of the celebrated Blattner-Montgomery duality theorem for , and as an application we establish the relationship between the homological dimensions of and A if H and its dual H* are both semisimple.
Christian Kassel (2013)
Annales mathématiques Blaise Pascal
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We define polynomial -identities for comodule algebras over a Hopf algebra and establish general properties for the corresponding -ideals. In the case is a Taft algebra or the Hopf algebra , we exhibit a finite set of polynomial -identities which distinguish the Galois objects over up to isomorphism.
Leonid F. Barannyk, Dariusz Klein (2012)
Colloquium Mathematicae
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Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...
Leonid F. Barannyk (2012)
Colloquium Mathematicae
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Let K be a field of characteristic p > 0, K* the multiplicative group of K and a finite group, where is a p-group and B is a p’-group. Denote by a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module...
Justyna Kosakowska, Daniel Simson (2008)
Colloquium Mathematicae
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Let C be a coalgebra over an arbitrary field K. We show that the study of the category C-Comod of left C-comodules reduces to the study of the category of (co)representations of a certain bicomodule, in case C is a bipartite coalgebra or a coradical square complete coalgebra, that is, C = C₁, the second term of the coradical filtration of C. If C = C₁, we associate with C a K-linear functor that restricts to a representation equivalence , where is a coradical square complete hereditary...
Igor Nikolaev (2015)
Czechoslovak Mathematical Journal
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The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
Raymundo Bautista (2006)
Colloquium Mathematicae
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Let Λ be an artin algebra. We prove that for each sequence of non-negative integers there are only a finite number of isomorphism classes of indecomposables , the bounded derived category of Λ, with for all i ∈ ℤ and E(X) the endomorphism ring of X in if and only if , the bounded derived category of the category of all left Λ-modules, has no generic objects in the sense of [4].