In this brief note we would like to give the construction of a free commutative unital associative Nijenhuis algebra on a commutative unital associative algebra based on an augmented modified quasi-shuffle product. —————————————

The concept of a Hopf algebra originated in topology. Classically, Hopf algebras are defined on the basis of unital modules over commutative, unital rings. The intention of the present work is to study Hopf algebra formalism (§1.2) from a universal-algebraic point of view, within the context of entropic varieties. In an entropic variety, the operations of each algebra are homomorphisms, and ten...

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

In this paper, we make a study of the generalization of classical RiemannStieltjes integral in the pseudo-analysis framework. For that, we consider the generalized g-semiring with commutative generalized generated pseudoaddition and non-commutative generalized generated pseudo-multiplication. AMS2000 Subject Classification: 26A39.

Abstract We prove that every Novikov–Poisson algebra over a field of zero characteristic can be embedded into commutative conformal with derivation. As corollary, we show commutator Gelfand–Dorfman obtained from is special, i.e., embeddable differential Poisson algebra.

We characterize the category of injective *-homomorphisms between commutative C*-subalgebras of various C*-algebras, namely C*-algebras of operators on separable Hilbert spaces, any finite-dimensional C*-algebra, and any commutative C*-algebra.

Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something which can be called a descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different, commutative subalgebra of...

We discuss two versions of a conjecture attributed to M Barr The Harrison cohomology of a commutative algebra is known to coincide with the Andr e Quillen cohomology over a eld of characteristic zero but not in prime characteristics The conjecture is that a modi ed version of Harrison cohomology taking into account torsion always agrees with Andr e Quillen cohomology We give a counterexample De...

Let q be a Lie algebra over an algebraically closed field k of characteristic zero. The symmetric algebra S(q) has a natural structure of Poisson algebra, and our goal is to present a sufficient condition for the maximality of Poisson-commutative subalgebras of S(q) obtained by the argument shift method. Study of Poisson-commuttive subalgebras of S(q) has attracted much attention in the last ye...