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Keywords:
associative rings; unipotent elements
associative rings; unipotent elements
Summary:
Let $R$ be an associative ring with 1 and $R^{\times}$ the multiplicative group of invertible elements of $R$. In the paper, subgroups of $R^{\times}$ which may be regarded as analogues of the similitude group of a non-degenerate sesquilinear reflexive form and of the isometry group of such a form are defined in an abstract way. The main result states that a unipotent abstractly defined similitude must belong to the corresponding abstractly defined isometry group.
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