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dc.contributor.authorA. Adrian Albert
dc.date.accessioned2016-02-19T14:04:49Z
dc.date.available2016-02-19T14:04:49Z
dc.date.issued1939
dc.identifier.isbn
dc.identifier.issn
dc.identifier.urihttp://ir.nmu.org.ua/handle/GenofondUA/4913
dc.description.abstractThe first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.
dc.language.isoEnglish
dc.publisherAmerican Mathematical Society
dc.subjectМатематика\\Алгебра
dc.subjectMathematics\\Algebra
dc.subject.ddc
dc.subject.lcc
dc.titleStructure of algebras,
dc.typeother
dc.identifier.aichIB35GYSFJA2V4C5VZFPG7UNSTCF3KKDM
dc.identifier.crc32E3A8924A
dc.identifier.doi
dc.identifier.edonkey346E3F677D887F9BB6FB7C28B9C08217
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dc.identifier.udk
dc.identifier.bbk
dc.identifier.libgenid340441
dc.identifier.md52EF01C89B8C14DD7D4D10FDE98184882
dc.identifier.sha1QBD5FSOQLIQEN44NRJCHCQJXZNHTL52B
dc.identifier.tthR7RSYBHLVIUHKPKVN46GFAJ4O4Y24ONH4MCJRMY


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