A splitting theorem for ℱ-products
Algebraic de Morgan's laws for non-commutative rings
An Application of a Theorem of Ziegler.
Dually slender modules and steady rings.
Galois coverings and the problem of axiomatization of the representation type of algebras.
Localization of cliques and model theory. (Localisation des cliques et théorie des modèles.)
On countable von Neumann regular rings
Products of small modules
Module is said to be small if it is not a union of strictly increasing infinite countable chain of submodules. We show that the class of all small modules over self-injective purely infinite ring is closed under direct products whenever there exists no strongly inaccessible cardinal.
Representation-directed algebras form an open scheme
We apply van den Dries's test to the class of algebras (over algebraically closed fields) which are not representation-directed and prove that this class is axiomatizable by a positive quantifier-free formula. It follows that the representation-directed algebras form an open ℤ-scheme.
Representation-finite triangular algebras form an open scheme
Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
Shelah's Singular Compactness Theorem.
Алгебраически компактные модули и относительная гомологическая алгебра над ручными наследственными алгебрами.
Алгоритмические свойства свободных колец.
Группы обратимых элементов матричных колец
Инъективные минимальные модули
О граничной эквивалентности колец и матричных колец над ними
О кольцах Уорфилда
Переход от выводимости в классической теории множеств к выводимости в интуиционистской теории множеств для языка колец.
Сильно минимальные модули над дистстрибутивными справа кольцами
Финитно аппроксимируемая ассоциативная алгебра с неразрешимой проблемой равенства