We prove that any rigid additive symmetric monoidal category can be mapped to a abelian in universal way. This yields novel approach Grothendieck's standard conjecture D and Voevodsky's smash nilpotence conjecture.

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies between well known central extensions and central nilpotence on one hand, and abelian extensions and congruence solvability on the other hand. In particular, we show that a loop is congruence solvable (that is, an iterated...

In this paper, we study Novikov algebras satisfying nontrivial identities. We show that a algebra over field of zero characteristic satisfies identity some unexpected “universal” identities, in particular, right associator nilpotence, and nilpotence the commutator ideal. This, implies if only it is Lie-solvable. also establish any system identities follows from finitely many them, same holds fo...

We prove that if G is a finite 2-generated p-group of nilpotence class at most 2 then the group algebra with coefficients in field p elements determines up to isomorphisms.

In this paper, we find a condition that characterizes when two Camina p-groups of nilpotence class 2 form a Brauer pair. MSC primary: 20C15

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.

In this paper the authors discuss a relationship between ÿnite semiÿelds of characteristic p and certain ÿnite p-groups of nilpotence class 2.

The question about polynomial maps F : C → C, first raised by Keller [1] in 1939 for polynomials over the integers but now also raised for complex polynomials and, as such, known as The Jacobian Conjecture (JC), asks whether a polynomial map F with nonzero constant Jacobian determinant detF (x) need be a polyomorphism: Injective and also surjective with polynomial inverse. The known reductions ...