The Chern-Galois theory is developed for corings or coalgebras over non-commutative rings. As the first step the notion of an entwined extension as an extension of algebras within a bijective entwining structure over a non-commutative ring is introduced. A strong connection for an entwined extension is defined and it is shown to be closely related to the Galois property and to the equivariant p...

We introduce a theory of modules over representation small category taking values in entwining structures semiperfect coalgebra. This takes forward the aim developing categories entwined to same extent as that module well philosophy Mitchell working with rings several objects. The representations are motivated by work Estrada and Virili, who developed preadditive categories, which were then stu...

Orient and oriented character with the rare features and brilliant beauty attract the romantic writers. This attractiveness becomes more widespread in the works of creators of Russian historical novels particularly in long story “Sins by whom?“. This work has integrated in it several conflicting objectives. Attempting to depict realistic image in the work with the evident tension to...

The goddess of health, Hygieia, was much venerated, understandably, in the ancient Greek world; her numerous statues usually represented her holding a serpent. Hygieia's father was Aesculapius, the god of medicine, who developed his clinical skills as physician to the Argonauts and made use of herbs in treatment; the serpent and the cock were considered sacred to him. So the Greeks, when wantin...