Related papers: Ascending Chain Conditions in Free Baxter Algebras
We study progression-free sets in the abelian groups $G=(\mathbb{Z}_m^n,+)$. Let $r_k(\mathbb{Z}_m^n)$ denote the maximal size of a set $S \subset \mathbb{Z}_m^n$ that does not contain a proper arithmetic progression of length $k$. We give…
A class of algebras is constructed using free fermions and the invariant antisymmetric tensors associated with irreducible holonomy groups. (This version contains minor typographical corrections and some additional references. )
A free differential for an arbitrary associative algebra is defined as a differential with a uniqueness property. The existence problem for such a differential is posed. The notion of optimal calculi for given commutation rules is…
Certain weight-based orders on the free associative algebra $R = k<x_1, ..., x_t >$ can be specified by $t \times \infty$ arrays whose entries come from the subring of nonnegative elements in a totally ordered field. Such an array $A$…
Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join-semilattice were first considered by A.V. Figallo, G. Ramon and S. Saad in [11], and independently by S. Celani and D. Montangie in [7]. On the…
This paper presents the development of a new class of algorithms that accurately implement the preferential attachment mechanism of the Barab\'asi-Albert (BA) model to generate scale-free graphs. Contrary to existing approximate…
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…
We associate reduced and full C*-algebras to arbitrary rings and study the inner structure of these ring C*-algebras. As a result, we obtain conditions for them to be purely infinite and simple. We also discuss several examples.…
In this paper, we introduce the notion of free-free-Boolean independence relation for triples of algebras. We define free-free-Boolean cumulants ans show that the vanishing of mixed cumulants is equivalent to free-free-Boolean independence.…
We make use of a forcing technique for extending Boolean algebras. The same type of forcing was employed in [BK81], [Kos99], and elsewhere. Using and modifying a lemma of Koszmider, and using CH, we obtain an atomless BA, A such that f(A) =…
The free resolution and the Alexander dual of squarefree monomial ideals associated with certain subsets of distributive lattices are studied.
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.
A subset $S$ of vertices in a planar graph $G$ is a free set if, for every set $P$ of $|S|$ points in the plane, there exists a straight-line crossing-free drawing of $G$ in which vertices of $S$ are mapped to distinct points in $P$. In…
We study the cosmological evolution for a scalar field dark matter model, by considering a parameterization of the evolution equations that allow us to unify in a single parameter a family of potentials: quadratic (free case), trigonometric…
Involutive non-degenerate set theoretic solutions of the Yang-Baxter equation are considered, with a focus on finite solutions. A rich class of indecomposable and irretractable solutions is determined and necessary and sufficient conditions…
This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band…
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the Alexander dual is computed.
A necessary and sufficient condition is presented for a graph algebra to satisfy a bracketing identity. The associative spectrum of an arbitrary graph algebra is shown to be either constant or exponentially growing.
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-element set satisfying a condition. A condition is called chain-dependent, if it is satisfied for a family if and only if it is satisfied for…