Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry最新文献_第2页

On the structure space of a direct product of rings 关于环的直积的结构空间

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1970-01-01 DOI: 10.32917/HMJ/1206138227

Kanroku Aoyama

引用次数: 10

On the structure of bialgebras attached to group varieties 论群变异上的双代数的结构

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1970-01-01 DOI: 10.32917/HMJ/1206138378

H. Yanagihara

引用次数: 1

Notes on derivations of higher order 关于高阶导数的注意事项

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138584

Shizuka Sato

引用次数: 2

On the odd order non-singular immersions of real projective spaces. 实射影空间的奇阶非奇浸入。

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138528

Teiichi Kobayashi

引用次数: 5

A generalization of Kuhn's theorem for an infinite game 无限对策下库恩定理的推广

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138533

Masayuki Takahashi

引用次数: 1

On the decomposition of a linearly connected manifold with torsion. 带扭转线性连接流形的分解。

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138581

M. Kikkawa

{"title":"On the decomposition of a linearly connected manifold with torsion.","authors":"M. Kikkawa","doi":"10.32917/HMJ/1206138581","DOIUrl":"https://doi.org/10.32917/HMJ/1206138581","url":null,"abstract":"Let M be a differentiable manifold with a linear connection, and let Φx be the homogeneous holonomy group at a point % e M. If the tangent vector space at x is decomposed into a direct sum of subspaces which are invariant under Φx, then by the parallel displacements along curves on M, parallel distributions are defined on M corresponding to those subspaces. If M is a Riemannian manifold and its connection is Riemannian, then by the de Rham decomposition theorem (Q7] or [_4Γ p. 185) the above parallel distributions are completely integrable and, at any point, M is locally isometric to the direct product of leaves through the point. Moreover, if M is simply connected and complete, it is globally isometric to the direct product of those leaves (see also [7] or [4] p. 192). The above local and global decomposition theorems of de Rham are generalized to the case of pseudo-Riemannian manifold by H. Wu ([9]). On the other hand, in [2], S. Kashiwabara generalized the global decomposition theorem to the case of linearly connected manifold without torsion, under the assumption of local decomposability. In the present paper, a linearly connected manifold with torsion will be treated and a condition of local decomposition will be given in terms of curvature and torsion (Theorem 1). Next, in §4, the results will be applied to a reductive homogeneous space with the canonical connection of the second kind, using the notion of algebra introduced by A. A. Sagle in [8]. Finally, in § 5, we shall remark about the decomposition of a local loop with any point in M as its origin (£3]), corresponding to the local decomposition of the linearly connected manifold M. The author wishes to express his hearty thanks to Prof. K. Morinaga for his kind suggestions and encouragement during the preparation of this paper at Hiroshima University.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"26 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76885504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

A remark on the homeomorphism group of a manifold 关于流形的同胚群的注解

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138587

Y. Nomura

引用次数: 0

A theorem on characteristically nilpotent algebras 关于特征幂零代数的一个定理

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138529

S. Tôgô

{"title":"A theorem on characteristically nilpotent algebras","authors":"S. Tôgô","doi":"10.32917/HMJ/1206138529","DOIUrl":"https://doi.org/10.32917/HMJ/1206138529","url":null,"abstract":"1. The notion of characteristic nilpotency of Lie algebras has been introduced by Dixmier and Lister [3] and studied by Leger and Togo [4]. Let L be a Lie algebra over a field Φ and ® (L) be the set of all derivations of L. Put L^ = LcS){L)={Σ1aiDiaie L, D{ e ®(Z,)} and define inductively ί ^ = £C»-^©(i) for n>2. L is called characteristically nilpotent provided there exists an integer k such that L = (0). Then every characteristically nilpotent Lie algebra is nilpotent. However, few similarities are known between the properties of nilpotent and characteristically nilpotent algebras, e.g., a subalgebra and a quotient algebra of a characteristically nilpotent Lie algebra are not necessarily characteristically nilpotent, contrary to the case of nilpotent algebras. Recently, in [_2~], C.-Y. Chao has shown a characterization of nilpotent Lie algebras: Let Lbea Lie algebra over a field Φ and TV be a nilpotent ideal of L. Then L is nilpotent if and only if L/N is nilpotent. The purpose of this note is to show a similar characterization of characteristically nilpotent Lie algebras, as a matter of fact, more generally of characteristically nilpotent nonassociative algebras. By a nonassociative algebra we mean an algebra which is not necessarily associative, that is, a distributive algebra [β'J. The definition of characteristic nilpotency of a nonassociative algebra A is obtained by replacing A instead of L in that of a Lie algebra stated above and this is due to the first version of the paper [ΊΓ] of T.S. Ravisankar. However, it has not yet been known that there actually exists a characteristically nilpotent nonassociative algebra which is not a Lie algebra. We shall show the existence of such an algebra in Section 3. All the algebras considered in this note are assumed to be finite dimensional over their base fields.","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"10 1","pages":"209-212"},"PeriodicalIF":0.0,"publicationDate":"1969-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89118391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Multiplication rings containing only finitely many minimal prime ideals 只包含有限个最小素数理想的乘法环

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138588

J. L. Mott

引用次数: 17

Relations between capacities and maximum principle 容量与最大原则之间的关系

Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry Pub Date : 1969-01-01 DOI: 10.32917/HMJ/1206138586

M. Yamasaki

引用次数: 2