Related papers: On free completely iterative algebras
Let $F$ be an infinite field and let $f$ be a nonzero multilinear polynomial with coefficients in $F$. We prove that for every positive integer $d$ there exists a positive integer $s$ such that $f(M_{s}(F))$, the image of $f$ in $M_{s}(F)$,…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper…
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
We study Frobenius extensions which are free-filtered by a totally ordered, finitely generated abelian group, and their free-graded counterparts. First we show that the Frobenius property passes up from a free-graded extension to a…
The central objective of this article is to provide an elementary proof of the following theorem, of which we are unaware of any trace in the existing literature. If $B$ is a net finite free algebra over a commutative ring $A$, then it is…
The algebraic extension $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}}$ of the extended bicyclic semigroup for an arbitrary $\omega$-closed family $\mathscr{F}$ subsets of $\omega$ is introduced. It is proven that…
A semi-Peano algebra is an algebra for which each operation is injective, and the images of the operations are pairwise disjoint. The most straightforward non-trivial kind of finitely presented semi-Peano algebra are algebras with a single…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
A combinatorial structure, $\mathcal{F}$, with counting sequence $\{a_n\}_{n\ge 0}$ and ordinary generating function $G_\mathcal{F}=\sum_{n\ge0} a_n x^n$, is positive algebraic if $G_\mathcal{F}$ satisfies a polynomial equation…
We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in…
We construct counterexamples to the conjecture that every free arrangement is recursively free in characteristic zero. The intersection lattice of our smallest example has a realization over a finite field which is recursively free, thus…
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
Fusion rules among irreducible modules of the free bosonic orbifold vertex operator algebra are completely determined.
We reduce the set of classic relational algebra operators to two binary operations: natural join and generalized union. We further demonstrate that this set of operators is relationally complete and honors lattice axioms.
In this note, we give a new characterization for an algebra to be $\qo$-compact in terms of {\em super-product operations} on the lattice of congruences of the relative free algebra.
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
Suppose that $h$ and $g$ belong to the algebra $\B$ generated by the rational functions and an entire function $f$ of finite order on ${\Bbb C}^n$ and that $h/g$ has algebraic polar variety. We show that either $h/g\in\B$ or $f=q_1e^p+q_2$,…
We extend Barr's well-known characterization of the final coalgebra of a $Set$-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a $Set$-monad $\mathbf{M}$ for functors arising as liftings.…