Indecomposable modules over noetherian rings and fixed point rings of rings of finite type

Hartman proved that a diffeomorphism is topologically conjugate to a linear map on a neighbourhood of a hyperbolic fixed point ([3]). In this paper we study the topological conjugacy problem of a diffeomorphism on a neighbourhood of a hyperbolic set, and prove that for any hyperbolic set there is an arbitrarily slight extension to which a sub-shift of finite type is semi-conjugate.

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ON THE FINITE TYPE OF FAMILIES OF INDECOMPOSABLE MODULES

Journal of Algebra and Its Applications ◽

10.1142/s0219498804000733 ◽

2004 ◽

Vol 03 (01) ◽

pp. 111-119

Author(s):

NGUYEN VIET DUNG

Keyword(s):

Finite Number ◽

Finite Type ◽

Direct Sums ◽

Indecomposable Modules ◽

Isomorphism Classes

We show that a family [Formula: see text] of indecomposable modules has only a finite number of non-isomorphic members if [Formula: see text] satisfies either of the following: (a) [Formula: see text] has a preinjective partition, and satisfies the artinian condition on morphisms between the Mi; (b) [Formula: see text] has a preprojective partition, and satisfies the noetherian condition on morphisms between the Mi. As a consequence, we recover some of recent results due to B. Huisgen-Zimmermann and M. Saorín [11], establishing the relationships between the endo-structure of infinite direct sums ⊕i∈IMi of indecomposable modules Mi and the finiteness of isomorphism classes of the Mi.

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ON AUTOMORPHISMS OF GENERALIZED CUNTZ ALGEBRAS

International Journal of Mathematics ◽

10.1142/s0129167x9800021x ◽

1998 ◽

Vol 09 (04) ◽

pp. 493-512 ◽

Cited By ~ 4

Author(s):

YOSHIKAZU KATAYAMA ◽

HIROAKI TAKEHANA

Keyword(s):

Fixed Point ◽

Finite Type ◽

Invertible Operator ◽

Cuntz Algebra ◽

Gauge Action ◽

Cuntz Algebras ◽

C Algebra ◽

Fixed Point Algebra

Let X be a full right Hilbert B-bimodule of finite type and [Formula: see text] be its generalized Cuntz algebra. We give a notion that the C*-algebra B is X-aperiodic. We show that the fixed point algebra ℱX for a gauge action is simple if and only if the C*-algebra B is X-aperiodic. For a invertible operator U on X with some properties, a quasi-free automorphism αU of [Formula: see text] is defined. We give some conditions in order that αU is inner in the case that B is X-aperiodic. We apply them to the automorphism αU on Cuntz–Krieger algebras.

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Fixed point rings of some non noetherian rings

Communications in Algebra ◽

10.1080/00927878608823300 ◽

1986 ◽

Vol 14 (1) ◽

pp. 109-124 ◽

Cited By ~ 2

Author(s):

S. J⊘ndrup

Keyword(s):

Fixed Point ◽

Noetherian Rings

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tCG torsion pairs

Journal of Algebra and Its Applications ◽

10.1142/s0219498819501275 ◽

2019 ◽

Vol 18 (07) ◽

pp. 1950127 ◽

Cited By ~ 1

Author(s):

Daniel Bravo ◽

Carlos E. Parra

Keyword(s):

Finite Type ◽

Text Structure ◽

Noetherian Rings ◽

Precise Description ◽

Torsion Pair ◽

Torsion Pairs ◽

Finitely Presented ◽

Regular Rings ◽

Compactly Generated

We investigate conditions when the [Formula: see text]-structure of Happel–Reiten–Smalø associated to a torsion pair is a compactly generated [Formula: see text]-structure. The concept of a [Formula: see text]CG torsion pair is introduced and for any ring [Formula: see text], we prove that [Formula: see text] is a [Formula: see text]CG torsion pair in [Formula: see text] if, and only if, there exists, [Formula: see text] a set of finitely presented [Formula: see text]-modules in [Formula: see text], such that [Formula: see text]. We also show that every [Formula: see text]CG torsion pair is of finite type, and show that the reciprocal is not true. Finally, we give a precise description of the [Formula: see text]CG torsion pairs over Noetherian rings and von Neumman regular rings.

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On the sofic limit sets of cellular automata

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385700008609 ◽

1995 ◽

Vol 15 (4) ◽

pp. 663-684 ◽

Cited By ~ 25

Author(s):

Alejandro Maass

Keyword(s):

Fixed Point ◽

Cellular Automata ◽

Cellular Automaton ◽

Finite Type ◽

Finite Time ◽

Limit Set ◽

Limit Sets ◽

One Dimensional ◽

Sofic System

AbstractIt is not known in general whether any mixing sofic system is the limit set of some one-dimensional cellular automaton. We address two aspects of this question. We prove first that any mixing almost of finite type (AFT) sofic system with a receptive fixed point is the limit set of a cellular automaton, under which it is attained in finite time. The AFT condition is not necessary: we also give examples of non-AFT sofic systems having the same properties. Finally, we show that near Markov sofic systems (a subclass of AFT sofic systems) cannot be obtained as limit sets of cellular automata at infinity.

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