Up to the present, there have been few strategies that are completely effective in treating undifferentiated somatoform disorder with tinnitus. We herein report that Yoku-kan-san (TJ-54), one of Japan's traditional herbal medicines, is an effective treatment for tinnitus in undifferentiated somatoform disorder complicated with headache and insomnia. TJ-54 has been also used as an effective treatment for insomnia and irritability in recent centuries and is considered to have some effects on the excitability of nerves. Further studies are needed to confirm the efficacies of Japanese herbal medicines.

A new model for Staebler-Wronski effects is proposed. Defect pairs of (D°:D+) or (D°:D°) as a precursor of neutral dangling bonds are produced by electron-phonon interactions. Most of the defect-pairs immediately rebond after creation, but some of them separate resulting in wandering dangling bonds. The separation and the wandering take place through bond-switching. When wandering dangling bonds collide, most of them make covalent bonds via defect-pairs. The rate equations based on these processes are given and annealing effects on photo-generated dangling bonds are studied.

In der Arbeit [2] hat L. Rédei den Begriff des einstufig nichtkommutativen Ringes eingefiihrt, und die alien möglichen Typen der einstufig nichtkommutativen endlichen Ringe aufgezàhlt. Sie bestehen aus drei Grundtypen und ihren homomorphen Bildern. In der oben genannten Arbeit hat Rédei einstufig nichtkommutativen unendlichen Ringes ganz kurz erwähnt, und nur darauf hingewiesen, dass man nicht einmal weiss, ob solche Ringe überhaupt existieren. In der vorliegenden Arbeit handelt es sich um die Nichtexistenz der einstufig nichtkommutativen unendlichen Ringe. Obwohl die Nichtexistenz der allge-meinen unendlichen Ringe vom genannten Charakter hoch glaubwürdig scheint, kann ich doch zur Zeit die Aufgabe in ihrer vollen Allgemeinheit nicht losen, sondem ich kann nur zeigen, dass ein einstufig nichtkommutativer Ring mit einer zusätzlichen Bedingung notwendigerweise endlich wird. Im folgenden soil nämlich der untenbenannte Satz bewiesen werden.

In the previous paper [3] the author has shown a possibility to construct a series of sfields by taking sfields of quotients of split crossed products of a sfield. In this paper the same problem is treated, and, by considering general crossed products, a generalization of the previous result is given: Let K be a sfield and G be the join of a well-ordered ascending chain of groups Gα of outer automorphisms of K such that a) G1 is the identity automorphism group, b) Gα is a group extension of Gα-1 by a torsion-free abelian group for each non-limit ordinal α, and c) for each limit ordinal α. Then an arbitrary crossed product of K with G is an integral domain with a sfield of quotients Q and the commutor ring of K in Q coincides with the centre of K.

In [5], Ikeda-Nagao-Nakayama gave a characterization of algebras of cohomological dimension ≦n In a subsequent paper [4] Eilenberg gave an alternative treatment of the same question. The present paper is devoted to the discussion of a number of questions suggested by the results of [4] and [5]. Among others it is shown that the conditions employed in stating the main results in [4] and [5] are equivalent, so that the main results of these two papers are in accord. Further, the cohomological dimension of a residue-algebra is studied in terms of that of the original algebra and the (module-) dimension of the associated ideal. The terminology and notation employed here are that of [3].

Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:

Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.

Cohomology groups of (associative) algebras have been introduced (for higher dimensions) and studied by G. Hochschild in his papers [2], [3] and [4]. 1-, 2-, and 3-dimensional cohomology groups are in closest connection with some classical properties of algebras. In particular, an algebra is absolutely segregated. if and only if its 2-dimensional cohomology groups are all trivial. It is thus of use and importance to determine the structure of algebras with universally vanishing 2-cohomology groups, i.e. absolutely segregated algebras; they form a class which is wider than the class of all algebras with universally vanishing 1-cohomology groups, i.e. separable algebras in the sense of the Dickson-Wed-derburn theorem.