相关论文: Varieties of De Morgan monoids: covers of atoms

For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A…

For a Grothendieck category having a noetherian generator, we prove that there are only finitely many minimal atoms. This is a noncommutative analogue of the fact that every noetherian scheme has only finitely many irreducible components.…

In this paper, we present complete classifications, up to isomorphism, of all two-element dimonoids, all commutative three-element dimonoids, and all abelian three-element dimonoids. We show that, up to isomorphism, there exist exactly 8…

It is well known that the subvariety lattice of the variety of relation algebras has exactly three atoms. The (join-irreducible) covers of two of these atoms are known, but a complete classification of the (join-irreducible) covers of the…

The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice $\mathbb{MON}$ of monoid varieties remains unknown.…

We prove that, up to isomorphism and anti-isomorphism, there are only two semigroups which are the union of two copies of the free monogenic semigroup. Similarly, there are only nine semigroups which are the union of three copies of the…

We study the finite basis problem for $4$-element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are $112$ such algebras. We show that $106$ of them are finitely…

De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain…

In this paper we study the subdirectly irreducible algebras in the variety ${\cal PCDM}$ of pseudocomplemented De Morgan algebras by means of their De Morgan $p$-spaces. We introduce the notion of $body$ of an algebra ${\bf L} \in {\cal…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

Let $M$ be a cancellative and commutative monoid (written additively). The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements (often called atoms in the literature). Weaker versions of…

We exhibit a 6-element semigroup that has no finite identity basis but nevertheless generates a variety whose finite membership problem admits a polynomial algorithm.

We prove that the symmetric group $S_n$ has a unique minimal cover $\mathcal{M}$ by maximal nilpotent subgroups, and we obtain an explicit and easily computed formula for the order of $\mathcal{M}$. In addition, we prove that the order of…

For a group $G$ acting on an affine variety $X$, the separating variety is the closed subvariety of $X\times X$ encoding which points of $X$ are separated by invariants. We concentrate on the indecomposable rational linear representations…

While dealing with the nontrivial task of classifying Mueller matrices, of special interest is the study of the degenerate Mueller matrices (matrices with vanishing determinant, for which the law of multiplication holds, but there exists no…

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…

An affine manifold is a manifold with an affine structure, i.e. a torsion-free flat affine connection. We show that the universal cover of a closed affine 3-manifold $M$ with holonomy group of shrinkable dimension (or discompacit\'e in…

We introduce the notion of Universally Decodable Matrices of Genus g (UDMG), which for g=0 reduces to the notion of Universally Decodable Matrices (UDM) introduced in [8]. A UDMG is a set of L matrices over a finite field, each with K rows,…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field, and ${\Bbb S}$ a finite sequence of simple left $\Lambda$-modules. In [6, 9], quasiprojective algebraic varieties with accessible affine open covers were…

The Davis hyperbolic four-manifold $\mathcal{D}$ is not almost-complex, so that its Seiberg-Witten invariants corresponding to zero-dimensional moduli spaces are vanishing by definition. In this paper, we show that all the Seiberg-Witten…