相关论文: Limit varieties of aperiodic monoids with commutin…
A variety of algebras is called Cross if it is finitely based, finitely generated, and has finitely many subvarieties. In present article, we classify all Cross varieties of aperiodic monoids with commuting idempotents.
A variety of universal algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. Until recently, only two explicit examples of limit varieties of monoids, constructed by Jackson, were known.…
A monoid is aperiodic if all its subgroups are trivial. We completely classify all varieties of aperiodic monoids whose subvariety lattice is distributive.
We completely classify all varieties of aperiodic monoids with commuting idempotents whose subvariety lattice is distributive.
A limit variety is a variety that is minimal with respect to being non-finitely based. We present a new limit variety of aperiodic monoid. We also show that if there exists any other limit variety of aperiodic monoids, then it is contained…
A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show that together with the five limit varieties of monoids…
We completely classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive.
A limit variety is a variety that is minimal with respect to being non-finitely based. Since the turn of the millennium, much attention has been given to the classification of limit varieties of aperiodic monoids. Seven explicit examples…
A limit variety is a variety that is minimal with respect to being non-finitely based. The two limit varieties of Marcel Jackson are the only known examples of limit varieties of aperiodic monoids. Our previous work had shown that there…
We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We…
We give a classification of noncommutative algebraic monoid structures on normal affine varieties such that the group of invertible elements of the monoid is connected, solvable, and has a one-dimensional unipotent radical. We describe the…
We classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is finite or satisfies the descending chain condition or satisfies the ascending chain condition. It turns out that for varieties in this…
In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…
We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…
A monoid $M$ is called surjunctive if every injective cellular automata with finite alphabet over $M$ is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all…
In this short note we prove that any irreducible algebraic monoid whose unit group is an affine algebraic group is affine.
An algebraic variety $X$ is called rigid if there is no non-trivial action on $X$ of the additive group of the base field. A trinomial variety is an affine variety that is given by a set of equations consisting of polynomials with three…
The present paper is a continuation of \cite{jrz} and is devoted to the study of limit varieties of additively idempotent semirings. A limit variety is a nonfinitely based variety whose proper subvarieties are all finitely based. We present…
A commutative residuated lattice A is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It is proved here that epimorphisms are surjective…
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this…