Related papers: Generators of projective MV-algebras

General theory determines the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product…

In this document we consider the prime and maximal spectra of an MV-algebra with certain natural operations. Several new MV-algebras are constructed in this fashion.

If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on homomorphisms. This functor U always has a left adjoint F:…

We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators…

The aim of the paper is to study epicomplete objects in the category of $MV$-algebras. A relation between injective $MV$-algebras and epicomplete $MV$-algebras is found, an equivalence condition for an $MV$-algebra to be epicomplete is…

The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.

We propose in this article a definition of a MV-algebra structure on a class of subsets of some probability spaces and we work-out some examples. Our intention is to convey, by mean of the simplest possible examples, the idea that the…

In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface normally generates the (pure) mapping class group of the…

A number of papers deal with the problem of counting the number of retractions of a structure $S$ onto a substructure $T.$ In the particular case when $S$ is a free algebra, this number is $\geq 1$ iff $T$ is projective. In this paper we…

We establish the notion of a ``projective analytic vector'', whose defining requirements are weaker than the usual ones of an analytic vector, and use it to prove generation theorems for one-parameter groups on locally convex spaces. More…

The algebra of symmetric functions contains several interesting families of symmetric functions indexed by integer partitions or skew partitions. Given a sequence $\{u_n\}$ of symmetric functions taken from one of these families such that…

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…

We construct free cubic implication algebras with finitely many generators, and determine the size of these algebras.

We consider the operation of division in Pimenov algebras. We obtain necessary and sufficient conditions for prime elements in Pimenov algebras with a number of generators less than five. We adduce examples of the factorization of elements…

For a new class of algebras, called $EMV$-algebras, every idempotent element $a$ determines an $MV$-algebra which is important for the structure of the $EMV$-algebra. Therefore, instead of standard homomorphisms of $EMV$-algebras, we…

We give some general theorems on free algebras of varieties of Boolean algebras with operators; a hitherto new result is obtained for Pinter's substitution algebras. For n\geq 3, and m>1, there is a generating set of the free algebra freely…

We introduce the notion of a lower bound cluster algebra generated by projective cluster variables as a polynomial ring over the initial cluster variables and the so-called projective cluster variables. We show that under an acyclicity…

Let $K\langle X\rangle =K\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over a field $K$, and let $R\langle X\rangle =R\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over an arbitrary commutative ring…

We provide a framework connecting several well known theories related to the linearity of graded modules over graded algebras. In the first part, we pay a particular attention to the tensor products of graded bimodules over graded algebras.…

Let $k$ be a field and let $A=\bigoplus_{n\ge 1}A_n$ be a positively graded $k$-algebra. We recall that $A$ is graded nilpotent if for every $d\ge 1$, the subalgebra of $A$ generated by elements of degree $d$ is nilpotent. We give a method…