Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Zhevlakov K., Slin'ko A., Shestakov I. — Rings that are nearly associative Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Rings that are nearly associative Авторы: Zhevlakov K., Slin'ko A., Shestakov I. Аннотация: Until thirty years into this century the theory of rings developed mainly as the theory of associative rings. However, even in the middle of the last century there arose mathematical systems that satisfied all the axioms of a ring except associativity. For example, the algebra of Cayley numbers, which was constructed in 1845 by the English mathematician Arthur Cayley, is such a system. An identity found by Degen in 1818, which represents the product of two sums of eight squares again in the form of a sum of eight squares, was rediscovered by means of this algebra. The algebra of Cayley numbers is an eight-dimensional division algebra over the field of real numbers, which satisfies the following weakened identities of associativity: (m)b = a(&), (ab)b = a(bb). Algebras satisfying these two identities were subsequently named alternative. Such a name stems from the fact that in every algebra satisfying the two indicated identities, the associator (x, y, 2) = (xy)z - x(yz) is an alternating (skew-symmetric) function of its arguments. The theory of alternative algebras attracted the serious attention of mathematicians after the discovery of its deep connection with the theory of projective planes, which was actively developed at the beginning of this century. In this regard, it was discovered that alternative algebras are “sufficiently near” to associative ones. The essence of this nearness is exhibited by the theorem of Artin, which asserts that in every alternative algebra the subalgebra generated by any two elements is associative. Язык: Рубрика: Разное/ Статус предметного указателя: Неизвестно ed2k: ed2k stats Год издания: 1982 Количество страниц: 385 Добавлена в каталог: 01.07.2017 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020 | | О проекте