Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the
theory of algebras (in particular, noncommutative algebras) originated fromasingleexample …

This work covers the maximal and prime ideals of the incidence algebra, derivations and
isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions …

We describe automorphisms and derivations of the incidence coalgebra $\text {Co}(X, F) $ of
the partially ordered set $ X $ over a field $ F $. In this case, the fact is significantly used that …

Let P be a locally finite pre-ordered set, hereafter shortened to pre-ordered set, and let R be
a ring (with identity). The incidence ring I (P, R) consists of all functions f: PP--, R such that f …

Posets and poset homomorphisms (preserving both order and parallelism) have been
shown to form a category which is equivalent to the category of pogroupoids and their …

Let $\mathcal {R} $ be a commutative ring with unity, and let $ P $ be a locally finite poset.
The aim of the paper is to provide an explicit description of the additive biderivations of the …

Whether the following generalized version of Hilbert's Basis Theorem GHBT: C-Mod locally
noetherian→ C [X]-Mod locally noetherian, holds or not depends on the small category X …

J. Neggers, Hee Sik Kim ALGEBRAS ASSOCIATED WITH POSETS 1. Introduction Algebras
have been associated with a variety of differen Page 1 DEMONSTRATIO MATHEMATICA Vol …

An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a
finite set of orthogonal idempotents of R whose sum is 1. We show that, in the presence of …

Various properties (including evaluations of Möbius functions) and connections between 0-
locally finite combinatorial inverse monoids and quasi-Möbiusdivision categories are readily …