Can anyone help to find some information about these structures?
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1$\begingroup$ What is "algorithmically finite-dimensional algebra"? $\endgroup$– Boris NovikovMar 21, 2013 at 17:17
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$\begingroup$ A Google search for the term finds only this question. -- Maybe you could clarify what you are looking for. $\endgroup$– Stefan Kohl ♦Mar 21, 2013 at 17:21
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$\begingroup$ Possibly the term resulted from a translation from Russian(?) $\endgroup$– Stefan Kohl ♦Mar 21, 2013 at 17:23
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$\begingroup$ Yep. I translated it from Russian. So: 1. algorithmically finite (for groups) means that there is no algorithm for figuring infinite number of non-equal elements. 2. for algebras we consider this property as a algorithmically finite dimension. $\endgroup$– Ayrana MongushMar 21, 2013 at 17:45
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$\begingroup$ it's obvious for finite groups and algebras (and any other structures), but the point is that they should be infinite $\endgroup$– Ayrana MongushMar 21, 2013 at 17:51
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All what I could found is a talk of Bakhadyr Khoussainov
http://www.math.nsc.ru/conference/malmeet/11/plenary/2011MM_Khoussainov.ppt
in which he considered "algorithmically finite universal algebras". Maybe this will useful for you.