Journal of Algebra and Its Applications最新文献

This paper is devoted to the study of local and 2-local derivations of null-filiform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not derivations. We show that filiform and naturally graded quasi-filiform associative algebras admit 2-local derivations which are not derivations and any 2-local derivation of null-filiform associative algebras is a derivation.

We study a weak divisibility property for noncommutative rings: A nontrivial ring is fadelian if for all nonzero $a$ and $x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings and construct examples thereof which are not division rings, as well as non-Noetherian and non-Ore examples.

We prove that every profinite $n$-ary group $(G,f)={\mathrm{\text{der}}}_{𝜃,b}(G,•)$ has a unique Haar measure $m_p$ and further for every measurable subset $A\subseteq G$, we have $$m_p(A)=m(A)=(n-1)m^{\ast }(A),$$ where $m$ and $m^{\ast }$ are the normalized Haar measures of the profinite groups $(G,•)$ and the Post cover $G^{\ast }$, respectively.

The notion of semifunctor between categories, due to [9], is defined as a functor that does not necessarily preserve identities. In this paper, we study how several properties of functors, such as fullness, full faithfulness, separability, natural fullness, can be formulated for semifunctors. Since a full semifunctor is actually a functor, we are led to introduce a notion of semifullness (and then semifull faithfulness) for semifunctors. In order to show that these conditions can be derived from requirements on the hom-set components associated with a semifunctor, we look at “semisplitting properties” for seminatural tranformations and we investigate the corresponding properties for morphisms whose source or target is the image of a semifunctor. We define the notion of naturally semifull semifunctor and we characterize natural semifullness for semifunctors that are part of a semiadjunction in terms of semisplitting conditions for the unit and counit attached to the semiadjunction. We study the behavior of semifunctors with respect to (semi)separability and we prove Rafael-type Theorems for (semi)separable semifunctors and a Maschke-type theorem for separable semifunctors. We provide examples of semifunctors on which we test the properties considered so far.

We show that a previously introduced key exchange based on a congruence-simple semiring action is not secure by providing an attack that reveals the shared key from the distributed public information for any of such semirings.

In connection with the work of Malev published in [J. Algebra Appl.13 (2014) 1450004; J. Algebra Appl.20 (2021) 2150074], we continue to provide a classification of possible images of multilinear polynomials on generalized quaternion algebras.

For a pre-Lie–Yamaguti algebra $A$, by using its sub-adjacent Lie–Yamaguti algebra $A^c$, we are able to construct a semidirect product Lie–Yamaguti algebra via a representation of $A^c$. The investigation of such semidirect Lie–Yamaguti algebras leads us to the notions of para-Kähler structures and pseudo-Kähler structures on Lie–Yamaguti algebras, and also gives the definition of complex product structures on Lie–Yamaguti algebras. Furthermore, a Levi–Civita product with respect to a pseudo-Riemannian Lie–Yamaguti algebra is introduced and we explore its relation with pre-Lie–Yamaguti algebras.