Reduced finitary incidence algebras and their automorphisms

Let [Formula: see text] denote the incidence algebra of a locally finite poset [Formula: see text] over a field [Formula: see text] and [Formula: see text] some equivalence relation on the set of generators of [Formula: see text]. Then [Formula: see text] is the subset of [Formula: see text] of all the elements that are constant on the equivalence classes of [Formula: see text]. If [Formula: see text] satisfies certain conditions, then [Formula: see text] is a subalgebra of [Formula: see text] called a reduced incidence algebra. We extend this notion to finitary incidence algebras [Formula: see text] for any poset [Formula: see text]. We investigate reduced finitary incidence algebras [Formula: see text] and determine their automorphisms in some special cases.

Generalized Jordan Derivations of Incidence Algebras

For a given ring $\Re$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \Re)$ to be the incidence algebra of $X$ over $\Re$. Motivated by a Xiao’s result which states that every Jordan derivation of $I(X, \Re)$ is a derivation in the case $\Re$ is 2-torsion free, one proves that each generalized Jordan derivation of $I(X, \Re)$ is a generalized derivation provided $\Re$ is 2-torsion free, getting as a consequence the above mentioned result.

An Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra

In this paper, we introduce an algebra $\mathcal{H}$ from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra $\mathcal{H}$ and the quantum affine algebra $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$, where $q$ denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice and the quantum algebra $U_{q^{1/2}}(\mathfrak{sl}_2)$. We show that there exists an algebra homomorphism from $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$ to $\mathcal{H}$ and that any irreducible module for $\mathcal{H}$ is irreducible as an $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$-module.

Kongruensi Unsur Idempoten Ortogonal dalam Aljabar Insidensi Finitary

Let X be a partially ordered set, R is a commutative ring with identity and FININC (X, R) denote finitary incidencealgebra of poset X over R. In this paper it will be seen congruence of two elements that are idempotent orthogonalin FININC (X, R) relative to the modulo Radical Jacobson of algebra. Review of this topic would be useful to examineisomorphism problems of the finitary incidence Algebra.

GENERALIZED ARITHMETICAL FUNCTIONS OF THREE VARIABLES

The paper is devoted to the study of some properties of generalized arithmetical functions extended to the case of three variables. The convolution in this case is a convolution of the incidence algebra of a Möbius category in the sense of Leroux. This category is a two-sided analogue of the poset (it is viewed as a category) of positive integers ordered by divisibility.