The adjoint semigroup

1992 ◽  
pp. 1-18
Author(s):  
Jan van Neerven
Keyword(s):  
Adjoint Semigroup

Varieties satisfying semigroup identities: Algebras over a finite field and rings

2016 ◽  
Vol 26 (05) ◽  
pp. 985-1017
Author(s):  
Olga B. Finogenova
Keyword(s):  
Finite Field ◽  
Associative Algebras ◽  
Adjoint Semigroup ◽  
Semigroup Identities ◽  
Associative Rings

We study varieties of associative algebras over a finite field and varieties of associative rings satisfying semigroup or adjoint semigroup identities. We characterize these varieties in terms of “forbidden algebras” and discuss some corollaries of the characterizations.

NILPOTENT LINEAR SEMIGROUPS

2006 ◽  
Vol 16 (01) ◽  
pp. 141-160 ◽  
Author(s):  
ERIC JESPERS ◽  
DAVID RILEY
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Associative Algebra ◽  
Burnside Problem ◽  
Finitely Generated ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Adjoint Semigroup ◽  
Restricted Burnside Problem ◽  
Global And Local

We characterize the structure of linear semigroups satisfying certain global and local nilpotence conditions and deduce various Engel-type results. For example, using a form of Zel'manov's solution of the restricted Burnside problem we are able to show that a finitely generated residually finite group is nilpotent if and only if it satisfies a certain 4-generator property of semigroups we call WMN. Methods of linear semigroups then allow us to prove that a linear semigroup is Mal'cev nilpotent precisely when it satisfies WMN. As an application, we show that a finitely generated associative algebra is nilpotent when viewed as a Lie algebra if and only if its adjoint semigroup is WMN.

scholarly journals Relationship between ideals of BCI-algebras and order ideals of its adjoint semigroup

2001 ◽  
Vol 28 (9) ◽  
pp. 535-543 ◽  
Author(s):  
Michiro Kondo
Keyword(s):  
Open Problem ◽  
Order Ideal ◽  
Adjoint Semigroup ◽  
Order Ideals ◽  
One To One ◽  
The Relationship

We consider the relationship between ideals of a BCI-algebra and order ideals of its adjoint semigroup. We show that (1) ifIis an ideal, thenI=M−1(M(I)), (2)M(M−1(J))is the order ideal generated byJ∩R(X), (3) ifXis a BCK-algebra, thenJ=M(M−1(J))for any order idealJofX, thus, for each BCK-algebraXthere is a one-to-one correspondence between the setℐ(X)of all ideals ofXand the set𝒪(X)of all order ideals of it, and (4) the orderM(M−1(J))is an order ideal if and only ifM−1(J)is an ideal. These results are the generalization of those denoted by Huang and Wang (1995) and Li (1999). We can answer the open problem of Li affirmatively.

On Associative Rings with Locally Nilpotent Adjoint Semigroup

2003 ◽  
Vol 31 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Bernhard Amberg ◽  
Yaroslav Sysak
Keyword(s):  
Adjoint Semigroup ◽  
Locally Nilpotent ◽  
Associative Rings

THE ADJOINT SEMIGROUP OF A RING

2002 ◽  
Vol 30 (9) ◽  
pp. 4507-4525 ◽  
Author(s):  
Xiankun Du
Keyword(s):  
Adjoint Semigroup
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