## The group of automorphisms of semigroup End(P[X]) (2004)

### BibTeX

@MISC{Berzins04thegroup,

author = {A. Berzins},

title = {The group of automorphisms of semigroup End(P[X])},

year = {2004}

}

### OpenURL

### Abstract

In this paper is proved that the group of automorphisms of semigroup End(P[X]), if P is algebraically closed field, is generated by semi-inner automorphisms. 1

### Citations

18 | with the same (algebraic geometry
- Plotkin
- 2003
(Show Context)
Citation Context ...aper may be useful to describe the group Aut(End(Wn)) for different varieties of algebras over the field. 2 Definitions Let us recall some definitions for variety of commutative algebras Com − P (see =-=[4, 10]-=- for general case). 2Definition 2.1 Let P[X]) = P[x1, . . .,xn] be a free commutative algebra over a field P with a finite set of generators and τ ∈ Aut(EndP[X]). It is known [4] that there exists a ... |

17 | Varieties of algebras and algebraic varieties. Categories of algebraic varieties - Plotkin - 1996 |

14 |
E.Plotkin, Automorphisms of the category of free Lie algebras
- Mashevitzky
(Show Context)
Citation Context ...oncept of quasiinner automorphism - basic concept for description of Aut(End(W)) and Aut(Θ 0 ). Later groups Aut(Θ 0 ) were described for categories of free Lie algebras and free associative algebras =-=[1, 5, 6]-=-. Some other definition of quasiinner automorphism was used in mentioned papers. Also are described Aut(Θ 0 ) for varieties of groups, semigroups and some another varieties. For some varieties is desc... |

13 | Algebraic logic, varieties of algebras and algebraic varieties - Plotkin |

6 | The group of automorphisms of the category of free associative algebra
- Berzins
- 2004
(Show Context)
Citation Context ...oncept of quasiinner automorphism - basic concept for description of Aut(End(W)) and Aut(Θ 0 ). Later groups Aut(Θ 0 ) were described for categories of free Lie algebras and free associative algebras =-=[1, 5, 6]-=-. Some other definition of quasiinner automorphism was used in mentioned papers. Also are described Aut(Θ 0 ) for varieties of groups, semigroups and some another varieties. For some varieties is desc... |

6 | Automorphisms of categories of free modules and free Lie algebras
- Lipyanski
- 2005
(Show Context)
Citation Context ...oncept of quasiinner automorphism - basic concept for description of Aut(End(W)) and Aut(Θ 0 ). Later groups Aut(Θ 0 ) were described for categories of free Lie algebras and free associative algebras =-=[1, 5, 6]-=-. Some other definition of quasiinner automorphism was used in mentioned papers. Also are described Aut(Θ 0 ) for varieties of groups, semigroups and some another varieties. For some varieties is desc... |

3 | Varieties of algebras and algebraic varieties - Plotkin - 1996 |

2 |
The automorphisms of EndK[x], Proc
- Berzins
(Show Context)
Citation Context ...Aut(End(W)), where Θ 0 is the category of algebras W = W(X) with the finite X that are free in Θ, and W is a free algebra in Θ. Structure of Aut(Com − P)) 0 (i.e, the classical case) was described in =-=[2]-=-. Here was introduced variant of the concept of quasiinner automorphism - basic concept for description of Aut(End(W)) and Aut(Θ 0 ). Later groups Aut(Θ 0 ) were described for categories of free Lie a... |

2 | Geometric equivalence of algebras, Int - Berzins |

2 |
Algebraic geometry in Varieties with the Given Algebra of constants
- Berzins, Plotkin, et al.
- 2000
(Show Context)
Citation Context ...aper may be useful to describe the group Aut(End(Wn)) for different varieties of algebras over the field. 2 Definitions Let us recall some definitions for variety of commutative algebras Com − P (see =-=[4, 10]-=- for general case). 2Definition 2.1 Let P[X]) = P[x1, . . .,xn] be a free commutative algebra over a field P with a finite set of generators and τ ∈ Aut(EndP[X]). It is known [4] that there exists a ... |