TY - JOUR

T1 - On radicals of Novikov algebras

AU - Панасенко, Александр Сергеевич

N1 - This work was supported by the Program of fundamental scientific researches of Russian Academy of Sciences, project FWNF-2022-0002.

PY - 2024/1

Y1 - 2024/1

N2 - We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and the largest left quasiregular ideal coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras.

AB - We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and the largest left quasiregular ideal coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras.

KW - алгебра Новикова

KW - радикал

KW - первичная алгебра

KW - полупервичная алгебра

KW - конечномерная алгебра

KW - квазирегулярный идеал

KW - Novikov algebra

KW - finite dimensional algebra

KW - prime algebra

KW - quasiregular ideal

KW - radical

KW - semiprime algebra

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85165487360&origin=inward&txGid=cdeb557afd4229ea5f28e9aa54ed1eda

UR - https://www.mendeley.com/catalogue/d153c3fe-3bdb-3126-a97e-28c274f00803/

U2 - 10.1080/00927872.2023.2235420

DO - 10.1080/00927872.2023.2235420

M3 - Article

VL - 52

SP - 140

EP - 147

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 1

ER -