A direct factor theorem for commutative group algebras
Suppose is a field of characteristic and is a -primary abelian -group. It is shown that is a direct factor of the group of units of the group algebra .
A double chain of coupled circuits in analogy with mechanical lattices.
A dyadic view of rational convex sets
Let be a subfield of the field of real numbers. Equipped with the binary arithmetic mean operation, each convex subset of becomes a commutative binary mode, also called idempotent commutative medial (or entropic) groupoid. Let and be convex subsets of . Assume that they are of the same dimension and at least one of them is bounded, or is the field of all rational numbers. We prove that the corresponding idempotent commutative medial groupoids are isomorphic iff the affine space ...
A factorization of quasiorder hypergroups
The contribution is devoted to the question of the interchange of the construction of a quasiorder hypergroup from a quasiordered set and the factorization.
A Family of Bisimple Inverse Semigroups.
A family of critically finite maps with symmetry.
The symmetric group Sn acts as a reflection group on CPn-2 (for n>=3).Associated with each of the (n2) transpositions in Sn is an involution on CPn-2 that pointwise fixes a hyperplane -the mirrors of the action. For each such action, there is a unique Sn-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations...
A family of totally ordered groups with some special properties
Let be a field with a Krull valuation and value group , and let be the valuation ring. Theories about spaces of countable type and Hilbert-like spaces in [1] and spaces of continuous linear operators in [2] require that all absolutely convex subsets of the base field should be countably generated as -modules.By [1] Prop. 1.4.1, the field is metrizable if and only if the value group has a cofinal sequence. We prove that for any fixed cardinality , there exists a metrizable field ...
A Filtration for Rational Modules.
A Filtration of Schur Multiplicator.
A - finite actions and their automorphism groups.
A Finitely Presented Solvable Group that is not Residually Finite.
A finiteness condition for finitely generated semigroups.
A finiteness condition for finitely generated semigroups.
A finiteness condition for semigroups which generalizes Green-Rees' theorem.
A finiteness condition on automorphism groups
A finiteness property and an automatic structure for Coxeter groups.
A fixed point characterization of cofinite languages.
A flat manifold with no symmetries.
A flat plane that is not the limit of periodic flat planes.
A free group acting without fixed points on the rational unit sphere