This work is concerned with the question of when a von Neumann regular ring is expressible as a directed union of Artinian subrings.

We show that monotone σ -complete effect algebras under some conditions are σ - homomorphic images of effect-tribes (as monotone σ -complete effect algebras), which are nonempty systems of fuzzy sets closed under complements, sums of fuzzy sets less than 1, and containing all pointwise limits of nondecreasing fuzzy sets. Because effect-tribes are generalizations of Boolean σ -algebras of subsets, we present a generlization of the Loomis-Sikorski theorem for such effect algebras. We show that we can choose an effect-tribe to be a system of affin fuzzy sets. In addition, we present a new version of the Loomis-Sikorski theorem for σ-complete MV-algebras.

In this paper, we give certain analytic functional relations for the double harmonic series related to the double Euler numbers. These can be regarded as continuous generalizations of the known discrete relations obtained by the author recently.

We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomial D(x) whose square root generates a quadratic function field with non-trivial unit. We detail the genus I case.

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of R into R(N)R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is quasi-injective. The following results are obtained: M is quasi-injective if and only if M is pseudo-injective and M2 is CS. Furthermore, if M is a direct sum of uniform modules, then M is quasi-injective if and only if M is pseudo-injective. As a consequence of this it is shown that over a right Noetherian ring R, quasi-injective modules are precisely pseudo-injective CS modules.

The aim of this work is to offer a new characterization of the Hilbert symbol Q*p from the commutator of a certain central extension of groups. We obtain a characterization for Q*p (p≠2) and a different one for Q*2.

We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.

Let A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2: n; ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2: n; ω2) with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).