Free commutative two-step-associative algebras

被引：0

作者：

Ismailov, Nurlan ^{[1
]}

Shestakov, Ivan ^{[2
,3
]}

Zhang, Zerui ^{[4
]}

机构：

[1] Astana IT Univ, Astana, Kazakhstan

[2] Univ Sao Paulo, Inst Matemat & Stat, Sao Paulo, Brazil

[3] Sobolev Inst Math, Novosibirsk, Russia

[4] South China Normal Univ, Sch Math Sci, Guangzhou, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 12期

基金：

巴西圣保罗研究基金会;

关键词：

Automorphism; commutative two-step-associative algebra; Jacobian matrix; AUTOMORPHISMS; RINGS;

D O I：

10.1080/00927872.2024.2362345

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct linear bases for free commutative two-step-associative algebras and study their automorphisms. It turns out that every automorphism of a polynomial algebra without unit can be lifted to an automorphism of a free commutative two-step-associative algebra. Moreover, for any n >= 2, a wild automorphism is constructed for the n-generated free commutative two-step-associative algebra which is not stably tame and cannot be lifted to an automorphism of the n-generated free commutative nonassociative algebra.

引用

页码：4992 / 5004

页数：13

共 50 条

[31] ON COMMUTATIVE POWER-ASSOCIATIVE ALGEBRAS OF DEGREE-2
ALBERT, AA
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 74 (MAR) : 323 - 343
[32] Curvilinear Integral Theorems for Monogenic Functions in Commutative Associative Algebras
V. S. Shpakivskyi
Advances in Applied Clifford Algebras, 2016, 26 : 417 - 434
[33] Three-dimensional associative non-commutative algebras
Pickert, G
JOURNAL OF ALGEBRA, 2000, 234 (02) : 280 - 290
[34] ON WEDDERBURN PRINCIPAL THEOREM FOR COMMUTATIVE POWER-ASSOCIATIVE ALGEBRAS
HEMMINGER, RL
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 121 (01) : 36 - +
[35] Commutative basic algebras and non-associative fuzzy logics
Michal Botur
Radomír Halaš
Archive for Mathematical Logic, 2009, 48 : 243 - 255
[36] Commutative basic algebras and non-associative fuzzy logics
Botur, Michal
Halas, Radomir
ARCHIVE FOR MATHEMATICAL LOGIC, 2009, 48 (3-4) : 243 - 255
[37] VARIETIES OF ASSOCIATIVE ALGEBRAS FOR WHICH THE GROUPOID OF SUBVARIETIES IS A COMMUTATIVE SEMIGROUP
GONCHIGDORZH, R
MALTSEV, YN
SIBERIAN MATHEMATICAL JOURNAL, 1982, 23 (02) : 162 - 167
[38] POWER-ASSOCIATIVE COMMUTATIVE ALGEBRAS OF DEGREE-2
KOKORIS, LA
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1952, 38 (06) : 534 - 537
[39] COMMUTATIVE NON-ASSOCIATIVE ALGEBRAS AND IDENTITIES OF DEGREE 4
OSBORN, JM
CANADIAN JOURNAL OF MATHEMATICS, 1968, 20 (04): : 769 - &
[40] Free commutative B-algebras
Sebandal, A.N.
Vilela, Jocelyn P.
Sebandal, A.N. (1alfilgen@gmail.com), 1600, Forum-Editrice Universitaria Udinese SRL (44): : 198 - 207

← 1 2 3 4 5 →