On duality over a certain divided power algebra with positive characteristic.
On elementary equivalence, isomorphism and isogeny
Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These results are applied to deduce new instances of “elementary equivalence implies isomorphism”: for all genus zero...
On equations and properties concerning some classes of chordal polygons.
On exponents of p-adic differential modules.
On extensions of the maximal cyclotomic field having a given classical Galois group.
On Finite Intersections of "Henselian Valued" Fields.
On finite linear groups stable under Galois operation.
On full cover property of ordered fields
On Galois cohomology and realizability of 2-groups as Galois groups II
In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2n, n ≥ 4, having a cyclic subgroup of order 2n−2, over fields containing a primitive 2n−3th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups....
On Galois cohomology and realizability of 2-groups as Galois groups
In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.
On generalized gamma near-fields.
On generalized “ham sandwich” theorems
In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let be subsets with finite Lebesgue measure. Then, for any sequence of -linearly independent polynomials in the polynomial ring there are real numbers , not all zero, such that the real affine variety simultaneously bisects each of subsets , . Then some its applications are studied.
On generalized -adic integration
On generalized Redei functions.
On Geometric Embedding Problems and Semiabelian Groups.
On Grothendieck's pairing of component groups in the semistable reduction case.
On group-permutation polynomials
On Grunwald-Wang's theorem.
On Hopf Galois structures and complete groups.
On Ideal Theory in High Prufer Domains.