Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. Its is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and various deformations of the classical sequence...

In this paper we analyze and study the Smarandache idempotents (S-idempotents) in the ring Zn and in the group ring ZnG of a finite group G over the finite ring Zn. We have shown the existance of Smarandache idempotents (S-idempotents) in the ring Zn when n = 2 p (or 3p), where p is a prime > 2 (or p a prime > 3). Also we have shown the existance of Smarandache idempotents (S-idempotents) in th...

In this paper, we investigate idempotents in quandle rings and relate them with coverings. We prove that integral of quandles finite type are nontrivial coverings over nice base admit infinitely many idempotents, give their complete description. show the set all these forms a itself. As an application, deduce ring knot long idempotents. consider free products have only trivial giving infinite f...

We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents wh...

We introduce a new q-exponential/logarithm correspondance that allows us to solve a conjecture relating Zassenhauss Lie idempotents with other Lie idempotents related to the q-bracketing operator.

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types with aim providing an inductive step towards proof Firstly show that if algebra $\Lambda$ is triangular respect to a system non necessarily primitive idempotents, and at idempotents belong H$, then in H$. Secondly consider $2\times 2$ matrix algebra, on diagonal, projective bimodules corners...

Commutative H *-algebra is characterized in terms of idempotents. Here we offer three characterizations. 1. Introduction. In the past, the author used commuting idempotents to characterize continuous functions defined on a certain space [3, 4]. For example , it was shown in [3] that a certain Banach algebra is isometrically isomorphic to the space C(S) of all continuous complex-valued functions...

The biquaternion (complexified quaternion) algebra contains idempotents (elements whose square remains unchanged) and nilpotents (elements whose square vanishes). It also contains divisors of zero (elements with vanishing norm). The idempotents and nilpotents are subsets of the divisors of zero. These facts have been reported in the literature, but remain obscure through not being gathered toge...

We combine Young idempotents in the group algebra of the symmetric group with the action of the symmetric group on products of Vandermonde determinants to obtain idempotents with polynomial coefficients.

We study idempotents in intensional Martin-Löf type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky’s univalence axiom, there exist idempotents that do not split; thus in plain MLTT not all idempotents can be proven to split. On the other hand, assuming only function extensionality, an idempotent can b...