Some extensions of the notion of loop Grassmannians

We report an ongoing attempt to establish in algebraic geometry certain analogues of topological ideas, The main goal is to associate to a scheme X over a commutative ring k its “relative motivic homology” which is again an algebro geometric object over the base k. This is motivated by Number Theory, so the Poincaré duality for this relative motivic homology should be an algebro geometric incarnation of Class Field Theory

On some properties of quasi-MV algebras and square root quasi-MV algebras, IV

In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasiMV algebras and √0quasi-MV algebras. In particular: we provide a new representation of arbitrary √0qMV algebras in terms of √0qMV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √0qMV varieties, proving that it is uncountable, providing equational bases for some of its members, as well as analysing a number of slices of special interest; we show that the variety of √0qMV algebras has the amalgamation property; we provide an axiomatisation of the 1-assertional logic of √0qMV algebras; lastly, we reconsider the correspondence between Cartesian √0qMV algebras and a category of Abelian lattice-ordered groups with operators first addressed in [10]

Priestley duality for MV-algebras and beyond

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions

Entropy on effect algebras with Riesz decomposition property II: MV-algebras

summary:We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes

The dual of compact ordered spaces is a variety

In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially ordered spaces and monotone continuous maps is a quasi-variety - not finitary, but bounded by $\aleph_1$. An open question was: is it also a variety? We show that the answer is affirmative. We describe the variety by means of a set of finitary operations, together with an operation of countably infinite arity, and equational axioms. The dual equivalence is induced by the dualizing object [0,1]