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## Colloquium Mathematicum

2000 | 83 | 2 | 231-265
Tytuł artykułu

### Properties of G-atoms and full Galois covering reduction to stabilizers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $End_R (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $End_R (B)$-module $(End_R (B))^*$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- ⊗_R B^*$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^U: \coprod_{B ∈ U} mod kG_B → mod(R/G)$ and $Ψ^U: mod(R/G) → \prod_{B ∈ U} mod kG_B$)is full (resp. strictly full) is studied (see Theorems A, B and 6.3).
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
231-265
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-10-12
poprawiono
1999-01-12
poprawiono
1999-10-25
Twórcy
autor
• Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
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• [3] P. Dowbor, On modules of the second kind for Galoiscoverings, Fund. Math. 149 (1996), 31-54.
• [4] P. Dowbor, Galois covering reduction to stabilizers, Bull. Polish Acad. Sci. Math. 44 (1996), 341-352.
• [5] P. Dowbor, The pure projective ideal of amodule category, Colloq. Math. 71 (1996), 203-214.
• [6] P. Dowbor, On stabilizers ofG-atoms of representation-tame categories, Bull. Polish Acad. Sci. Math. 46 (1998), 304-315.
• [7] P. Dowbor and S. Kasjan, Galois covering technique andnon-simply connected posets of polynomial growth, J. Pure Appl. Algebra, to appear.
• [8] P. Dowbor, H. Lenzing and A. Skowroński, Galois coveringsof algebras by locally support-finite categories, in: Lecture Notes in Math. 1177, Springer, 1986, 91-93.
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• [19] D. Simson, Socle reduction and socle projective modules,J. Algebra 108 (1986), 18-68.
• [20] D. Simson, Representations of bounded stratified posets,coverings and socle projective modules, in: Topics in Algebra, Banach CenterPubl. 26, Part 2, PWN, Warszawa, 1990, 499-533.
• [21] D. Simson, Right peak algebras of two-separate stratifiedposets, their Galois coverings and socle projective modules, Comm. Algebra 20 (1992), 3541-3591.
• [22] D. Simson, On representation typesof module categories and orders, Bull. Polish Acad. Sci. Math. 41 (1993), 77-93.
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• [24] A. Skowroński, Criteria for polynomialgrowth of algebras, Bull. Polish Acad. Sci. Math. 42 (1994), 173-183.
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Bibliografia
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