Finite generation properties of cohomology rings for infinite groups

We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [Formula: see text] is finitely generated [Formula: see text] is [Formula: see text] is, where [Formula: see text] is the dual extension of a monomial algebra [Formula: see text] and [Formula: see text] is the opposite algebra of [Formula: see text].

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New approaches to finite generation of cohomology rings

Journal of Algebra ◽

10.1016/j.jalgebra.2021.07.027 ◽

2021 ◽

Author(s):

Van C. Nguyen ◽

Xingting Wang ◽

Sarah Witherspoon

Keyword(s):

Finite Generation ◽

Cohomology Rings ◽

New Approaches

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On cohomology rings of infinite groups

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2006.05.015 ◽

2007 ◽

Vol 208 (3) ◽

pp. 1099-1102 ◽

Cited By ~ 2

Author(s):

Eli Aljadeff

Keyword(s):

Infinite Groups ◽

Cohomology Rings

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Finite generation of some cohomology rings via twisted tensor product and Anick resolutions

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2018.03.012 ◽

2019 ◽

Vol 223 (1) ◽

pp. 316-339

Author(s):

Van C. Nguyen ◽

Xingting Wang ◽

Sarah Witherspoon

Keyword(s):

Tensor Product ◽

Finite Generation ◽

Cohomology Rings ◽

Twisted Tensor Product

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Semigroups with few endomorphisms

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700006996 ◽

1969 ◽

Vol 10 (1-2) ◽

pp. 162-168 ◽

Cited By ~ 5

Author(s):

Vlastimil Dlab ◽

B. H. Neumann

Keyword(s):

Cyclic Group ◽

Finite Groups ◽

Automorphism Groups ◽

Infinite Groups ◽

Infinite Cyclic Group

Large finite groups have large automorphism groups [4]; infinite groups may, like the infinite cyclic group, have finite automorphism groups, but their endomorphism semigroups are infinite (see Baer [1, p. 530] or [2, p. 68]). We show in this paper that the corresponding propositions for semigroups are false.

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