Related papers: Semilattices, Canonical Embeddings and Representin…
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In…
A general result by Jackson (Flat algebras and the translation of universal Horn logic to equational logic, J. Symb. Log. 73(1) (2008) 90--128) implies that the lattice of all quasivarieties of groups of exponent dividing $n$ embeds into…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
A semigroup is called $E$-$separated$ if for any distinct idempotents $x,y\in X$ there exists a homomorphism $h:X\to Y$ to a semilattice $Y$ such that $h(x)\ne h(y)$. Developing results of Putcha and Weissglass, we characterize…
We prove that a semigroup S is a semilattice of rectangular bands and groups of order two if and only if it satisfies the identity x = xxx and for all x,y in S, xyx is in the set {xyyx,yyxxy}.
In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain…
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…
The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( \lambda_{1}+r\lambda_{2} ,r\lambda_{1}\lambda_{2}):…
In this article we introduce a new matroid invariant, a combinatorial analog of the topological zeta function of a polynomial. More specifically we associate to any ranked, atomic meet-semilattice L a rational function Z(L,s), in such a way…
Building upon the results of Jacobs, we show that the category OMLatLin of orthomodular lattices and linear maps forms a dagger category. For each orthomodular lattice X, we construct a Foulis m-semilattice Lin(X) composed of endomorphisms…
We construct a metrizable semitopological semilattice $X$ whose partial order $P=\{(x,y)\in X\times X:xy=x\}$ is a non-closed dense subset of $X\times X$. As a by-product we find necessary and sufficient conditions for the existence of a…
The concept of a $\lambda$-lattice was introduced by V. Sn\'a\v sel in order to generalize some lattice concepts for directed posets whose elements need not have suprema or infima. We extend the concept of semimodularity from lattices to…
We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…
Dedekind stated and proved the well-known fact that a lattice is modular if and only if it does not contain a pentagon as a sublattice. In this paper we consider a similar result in the literature for the case of certain class of modular…
We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we prove that, for commutative varieties, the properties of being cancellable and…
An element $x$ of a lattice $L$ is modular if $L$ has no five-element sublattice isomorphic to the pentagon in which $x$ would correspond to the lonely midpoint. In the present work, we classify all modular elements of the lattice of all…
A specialization semilattice is a join semilattice together with a coarser preorder $ \sqsubseteq $ satisfying an appropriate compatibility condition. If $X$ is a topological space, then $(\mathcal P(X), \cup, \sqsubseteq )$ is a…
In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
For finitely generated groups $G$ and $H$ equipped with word metrics, a translation-like action of $H$ on $G$ is a free action where each element of $H$ moves elements of $G$ a bounded distance. Translation-like actions provide a geometric…