TY - JOUR

T1 - Left Ideals of Semiprime Novikov Algebras

AU - Kotenkov, N. V.

AU - Panasenko, A. S.

N1 - Kotenkov, N.V., Panasenko, A.S. Left Ideals of Semiprime Novikov Algebras. Sib Math J 67, 93–98 (2026). https://doi.org/10.1134/S003744662601009X The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2026–0017).

PY - 2026/1

Y1 - 2026/1

N2 - We study left ideals of Novikov algebras.It is shown that the center and the associative center of an ideal of a semiprime Novikov algebra are inherited from the whole algebra.We prove that in a prime nonassociative Novikov algebra, every left ideal that does not lie in the right annihilator of the algebra is itself a prime nonassociative Novikov algebra.We also obtain a description of left ideals of a semiprime Novikov algebra.It is shown that a minimal left ideal of a Novikov algebra lies either in the center or in the associator ideal of the algebra.

AB - We study left ideals of Novikov algebras.It is shown that the center and the associative center of an ideal of a semiprime Novikov algebra are inherited from the whole algebra.We prove that in a prime nonassociative Novikov algebra, every left ideal that does not lie in the right annihilator of the algebra is itself a prime nonassociative Novikov algebra.We also obtain a description of left ideals of a semiprime Novikov algebra.It is shown that a minimal left ideal of a Novikov algebra lies either in the center or in the associator ideal of the algebra.

KW - 512.554

KW - Novikov algebra

KW - annihilator

KW - minimal ideal

KW - prime algebra

KW - semiprime algebra

UR - https://www.scopus.com/pages/publications/105028574289

UR - https://www.mendeley.com/catalogue/5506e7b0-7af4-32a1-b5ec-b1abbcee501f/

U2 - 10.1134/S003744662601009X

DO - 10.1134/S003744662601009X

M3 - Article

VL - 67

SP - 93

EP - 98

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -