Abstract

In this work the Belousov theorem on linearity of invertible algebras with the Schauffler \(\forall\exists(\forall)\)-identity is extended to regular division algebras for other associative \(\forall\exists(\forall)\)-identities. For the formulas at consideration, the Schauffler-type theorems are also proved. The results are applicable in cryptography (cf. [1–3]).

中文翻译：

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肖夫勒型定理

摘要

在这项工作中，关于具有 Schauffler \(\forall\exists(\forall)\) 的可逆代数线性的 Belousov定理被扩展到其他关联的正则除法代数\(\forall\exists(\forall)\) -身份。对于所考虑的公式，还证明了 Schauffler 型定理。结果适用于密码学（参见 [1-3]）。