The adjoint semigroup

Author(s):  
Jan van Neerven
Keyword(s):  
2016 ◽  
Vol 26 (05) ◽  
pp. 985-1017
Author(s):  
Olga B. Finogenova

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.


2006 ◽  
Vol 16 (01) ◽  
pp. 141-160 ◽  
Author(s):  
ERIC JESPERS ◽  
DAVID RILEY

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.


2001 ◽  
Vol 28 (9) ◽  
pp. 535-543 ◽  
Author(s):  
Michiro Kondo

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.


2003 ◽  
Vol 31 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Bernhard Amberg ◽  
Yaroslav Sysak

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

Sign in / Sign up

Export Citation Format

Share Document