We describe all central extensions of $3$-dimensional non-zero complex Zinbiel algebras. As a corollary, we have full classification $4$-dimensional non-trivial algebras and $5$-dimensional with $2$-dimensional annihilator, which gives the principal step in algebraic

A well known theorem of Duflo claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is generated by its intersection with the centre. For a Lie superalgebra this result fails to be true. For instance, in the case of the orthosymplectic Lie superalgebra osp(1, 2), Pinczon gave in [Pi] an example of a Verma module whose annihilator is not gene...

In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.

In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, provide four different producing Also introduce two parameters, the annihilator stabilizing index and socle index, which are useful tools in classification theory of these Finally, use moduli sets as a convenient way to describe isomorphism classes

This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.