Interior GE-Algebras

Journal of Mathematics ◽

10.1155/2021/6646091 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Jeong-Gon Lee ◽

Ravikumar Bandaru ◽

Kul Hur ◽

Young Bae Jun

Keyword(s):

Commutative Transitive

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.

Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups

Infinite Group Theory ◽

10.1142/9789813204058_0005 ◽

2017 ◽

pp. 81-93

Author(s):

B. Fine ◽

A.M. Gaglione ◽

D. Spellman

Keyword(s):

Commutative Transitive

Erratum to: A Classification of Conjugately Separated Abelian, Commutative Transitive and Restricted Gromov One-Relator Groups

Results in Mathematics ◽

10.1007/s00025-011-0128-7 ◽

2011 ◽

Vol 61 (3-4) ◽

pp. 421-422

Author(s):

Benjamin Fine ◽

Alexei Myasnikov ◽

Volkmar große Rebel ◽

Gerhard Rosenberger

Keyword(s):

One Relator Groups ◽

Commutative Transitive

Equations in Algebras

International Journal of Algebra and Computation ◽

10.1142/s0218196718400064 ◽

2018 ◽

Vol 28 (08) ◽

pp. 1517-1533 ◽

Cited By ~ 2

Author(s):

Olga Kharlampovich ◽

Alexei Myasnikov

Keyword(s):

Hyperbolic Groups ◽

Fundamental Groups ◽

Associative Algebras ◽

Relatively Hyperbolic Groups ◽

Transitive Groups ◽

Right Angled Artin Groups ◽

Graph Groups ◽

Commutative Transitive ◽

Relatively Hyperbolic ◽

Torsion Free

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.

A Classification of Conjugately Separated Abelian, Commutative Transitive, and Restricted Gromov One-Relator Groups

Results in Mathematics ◽

10.1007/s00025-007-0245-5 ◽

2007 ◽

Vol 50 (3-4) ◽

pp. 183-193 ◽

Cited By ~ 5

Author(s):

Benjamin Fine ◽

Alexei Myasnikov ◽

Volkmar große Rebel ◽

Gerhard Rosenberger

Keyword(s):

One Relator Groups ◽

Commutative Transitive

Simplicial cohomology of augmentation ideals in l1(G)

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091508000060 ◽

2010 ◽

Vol 53 (1) ◽

pp. 97-109

Author(s):

Yemon Choi

Keyword(s):

Hochschild Cohomology ◽

Decomposition Theorem ◽

Bounded Cohomology ◽

Canonical Inclusion ◽

Commutative Transitive

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.