Related papers: Free-algebra functors from a coalgebraic perspecti…

It is well known from universal algebra that, for every signature $\Sigma$, there exist algebras over $\Sigma$ which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping…

We study varieties of certain ordered $\Sigma$-algebras with restricted completeness and continuity properties. We give a general characterization of their free algebras in terms of submonads of the monad of $\Sigma$-coterms. Varieties of…

For an endofunctor $H$ on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on $Y$ as the coproduct of the final coalgebra for $H$ and the free $H$-algebra on $Y$. As a consequence, we…

If $F$ is a (not necessarily associative) monad on $Set$, then the natural transformation $F(A\times B)\to F(A)\times F(B)$ is surjective if and only if $F(\boldsymbol{1})=\boldsymbol{1}$. Specializing $F$ to $F_{\mathcal{V}}$, the free…

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. )

For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative completion of the free algebra is the free completely…

By the classical theorem of Weitzenboeck the algebra of constants (i.e., the kernel) of a nonzero locally nilpotent linear derivation of the polynomial algebra K[X] in d variables over a field K of characteristic 0 is finitely generated. As…

For every finitary monad $T$ on sets and every endofunctor $F$ on the category of $T$-algebras we introduce the concept of an ffg-Elgot algebra for $F$, that is, an algebra admitting coherent solutions for finite systems of recursive…

We investigate accessible subgroups of a profinite group $G$, i.e. subgroups $H$ appearing as vertex groups in a graph of profinite groups decomposition of $G$ with finite edge groups. We prove that any accessible subgroup $H \leq G$ arises…

Let $K$ be a field of characteristic zero, let $\sigma$ be an automorphism of $K$ and let $\delta$ be a $\sigma$-derivation of $K$. We show that the division ring $D=K(x;\sigma,\delta)$ either has the property that every finitely generated…

A free semigroup algebra S is the weak-operator-closed (non-self-adjoint) operator algebra generated by n isometries with pairwise orthogonal ranges. A unit vector x is said to be wandering for S if the set of images of x under…

For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\Sigma$-algebras, is a retract of an ultraproduct of finite $\Sigma$-algebras…

Consider a diagram $\cdots \to F_3 \to F_2\to F_1$ of algebraic systems, where $F_n$ denotes the free object on $n$ generators and the connecting maps send the extra generator to some distinguished trivial element. We prove that (a) if the…

Suppose we are given complex manifolds $X$ and $Y$ together with substacks $\mathcal{S}$ and $\mathcal{S}'$ of modules over algebras of formal deformation $\mathcal{A}$ on $X$ and $\mathcal{A}'$ on $Y$, respectively. Suppose also we are…

A binding group theorem is proved in the context of quantifier-free internality to the fixed field in difference-closed fields of characteristic zero. This is articulated as a statement about the birational geometry of isotrivial algebraic…

An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F be a free algebra of some variety A of linear algebras over K freely generated…

Let $K$ be a field and $F$ a free group. By a classical result of Cohn and Lewin, the free group algebra $K\left[F\right]$ is a free ideal ring (FIR): a ring over which the submodules of free modules are themselves free, and of a…

Given an arbitrary, finitely presented, residually finite group $\Gamma$, one can construct a finitely generated, residually finite, free-by-free group $M_\Gamma = F_\infty\rtimes F_4$ and an embedding $M_\Gamma \hookrightarrow (F_4\ast…

In this note we show that there exist a $2^\mathfrak{c}$-generated free algebra $\mathcal{S} \subset \mathbb{R}^\mathbb{R}$ of Riemann integrable functions and a free algebra $\mathcal{C} \subset \mathbb{R}^{[0,1]}$ of continuous functions,…