Geodesic
On groups of similitudes in associative rings
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 525-531

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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.
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.
Classification : 16U60, 20H25
Keywords: associative rings; unipotent elements 
Bashkirov, Evgenii L. On groups of similitudes in associative rings. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 4, pp. 525-531. http://geodesic.mathdoc.fr/item/CMUC_2008_49_4_a0/
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     title = {On groups of similitudes in associative rings},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {525--531},
     year = {2008},
     volume = {49},
     number = {4},
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     zbl = {1192.16034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_4_a0/}
}
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