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# Перегляд Algebra and Discrete Mathematics, 2003, № 3 за датою випуску

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• (Algebra and Discrete Mathematics, 2003)
In this article we study gyrogroups and left gyrogroups as transversals in some suitable groups to its subgroups. These objects were introduced into consideration in a connection with an investigation of analogies between ...
• (Algebra and Discrete Mathematics, 2003)
• (Algebra and Discrete Mathematics, 2003)
• (Algebra and Discrete Mathematics, 2003)
Let G be a group, Λ = L σ∈G Λσ a strongly graded ring by G, H a subgroup of G and ΛH = L σ∈H Λσ. We give a necessary and sufficient condition for the ring Λ/ΛH to be separable, generalizing the corresponding result ...
• (Algebra and Discrete Mathematics, 2003)
Let H be a finite dimentional Hopf algebra over a field k and H∗ the dual Hopf algebra of H. Then a commutator right H∗ -Galois extension B of BH is characterized in terms of the smash product B#H and some relationships ...
• (Algebra and Discrete Mathematics, 2003)
• (Algebra and Discrete Mathematics, 2003)
Various versions of the prediction principle called the “Black Box” are known. One of the strongest versions can be found in [EM]. There it is formulated and proven in a model theoretic way. In order to apply it to ...
• (Algebra and Discrete Mathematics, 2003)
A field F is n-real if −1 is not the sum of n squares in F. It is shown that a field F is m-real if and only if rank (AAt ) = rank (A) for every n × m matrix A with entries from F. An n-real field F is n-real closed ...
• (Algebra and Discrete Mathematics, 2003)
All H− and R− cross-sections of the full finite semigroup Tn of all transformations of the set N = {1, 2, . . . , n} are described.

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