A simple right-alternative superalgebra whose even part has zero multiplication is called singular. In the paper, finite-dimensional algebraically generated singular superalgebras with non-degenerate switch are introduced and studied. A special case of such algebras, namely, linearly generated superalgebras, was previously classified by the authors. The construction of the extended double is given in the paper and it is proved that an algebraically generated singular superalgebra with non-degenerate switch is an extended double. It is also shown that, for any number \(d\geq32\), there exists a d-dimensional extended double.

中文翻译：

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代数生成的超代数

一个简单的右替代超代数，其偶数部分的乘法为零称为奇异。本文介绍并研究了具有非退化开关的有限维代数生成奇异超代数。此类代数的一个特例，即线性生成的超代数，先前已被作者分类。文中给出了扩展对偶的构造，并证明了具有非退化开关的代数生成奇异超代数是扩展对偶。还表明，对于任何数\(d\geq32\)，都存在一个d维扩展双精度数。