On recognisable properties of associative algebrasстатья
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Аннотация:The paper considers computer algebra in a non-commutative setting. So far, suchinvestigations have been centred on the use of algorithms for equality and of universal properties of algebras. Here, the foundation of all computations is the presentation of the algebra under investigation by a finite number of generators subject to a finite number of defining relations, which satisfy the additional property of forming a Gröbner (or standard) basis. Such algebras are called s.f.p.—for standard finite presentation. It is shown that various algebraic properties, such as being finite-dimensional, nilpotent, nil, algebraic are algorithmically recognisable. When the defining relations are words in the generators, this is also shown to be the case, for the properties of being semi-simple, prime, semi-prime, etc.