commutative transitive
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2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jeong-Gon Lee ◽  
Ravikumar Bandaru ◽  
Kul Hur ◽  
Young Bae Jun

The concepts of (commutative, transitive, left exchangeable, belligerent, antisymmetric) interior GE-algebras and bordered interior GE-algebras are introduced, and their relations and properties are investigated. Many examples are given to support these concepts. A semigroup is formed using the set of interior GE-algebras. An example is given that the set of interior GE-algebras is not a GE-algebra. It is clear that if X is a transitive (resp., commutative, belligerent, and left exchangeable) GE-algebra, then the interior GE-algebra X , f is transitive (resp., commutative, belligerent, and left exchangeable), but examples are given to show that the converse is not true in general. An interior GE-algebra is constructed using a bordered interior GE-algebra with certain conditions, and an example is given to explain this.



2018 ◽  
Vol 28 (08) ◽  
pp. 1517-1533 ◽  
Author(s):  
Olga Kharlampovich ◽  
Alexei Myasnikov

We show that the Diophantine problem (decidability of equations) is undecidable in free associative algebras over any field and in the group algebras over any field of a wide variety of torsion free groups, including toral relatively hyperbolic groups, right-angled Artin groups, commutative transitive groups, the fundamental groups of various graph groups, etc.



2017 ◽  
pp. 81-93
Author(s):  
B. Fine ◽  
A.M. Gaglione ◽  
D. Spellman


2011 ◽  
Vol 61 (3-4) ◽  
pp. 421-422
Author(s):  
Benjamin Fine ◽  
Alexei Myasnikov ◽  
Volkmar große Rebel ◽  
Gerhard Rosenberger


2010 ◽  
Vol 53 (1) ◽  
pp. 97-109
Author(s):  
Yemon Choi

AbstractLet G be a discrete group.We give a decomposition theorem for the Hochschild cohomology of l1(G) with coefficients in certain G-modules. Using this we show that if G is commutative-transitive, the canonical inclusion of bounded cohomology of G into simplicial cohomology of l1(G) is an isomorphism.



2007 ◽  
Vol 50 (3-4) ◽  
pp. 183-193 ◽  
Author(s):  
Benjamin Fine ◽  
Alexei Myasnikov ◽  
Volkmar große Rebel ◽  
Gerhard Rosenberger


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