Department of Algebra
The algebra studies common properties of operations
and transformations with sets satisfying to some laws. These laws,
i.e.axioms, which defines these operations, can be completely different,
depending on a problem. In this case we get such algebraic objects, as
groups, rings, fields, alternative algebras, Lie algebras etc.
As a rule these, algebraic objects appears consensually, but by
consideration of deep problems of mathematics, physics, other sections of
science. For example, the concept of group appeared in algebra by
consideration of the solutions of algebraic equations in radicals (term "group" was defined
by Evarist Galois who has applied designed to them a group theory to the
solution of a concrete problem of algebraic equations).
The
heyday of algebraic researches on algebra in the Kazan
university began on 30-50-th years of 20th century. In that times began to work
outstanding mathematician - N.G.Chebotarev, member-correspondent of
Acadimy of Science in USSR, managing stand of algebra till 1947. The Kazan
school these years conducted radical researches on algebra received a
world admission. It has elaborated the theory of fields and
theory of Galois, theory of Lie groups and algebras (N.G.Chebotarev,
professor V.V.Morozov, who managed stand of algebra since
1947 till 1970, and also their schoolboys).
Now these traditions are prolonged
by V.V.Morozov schoolboys
U.B.Ermolaev, I.I.Sakhaev, and A.H. Dolotkazin and
also other employees of chair, who works in different areas of
algebra. On chair of algebra there are fruitful researches and
on other scientific direction - logic theory. At pre-revolutionary times
in Kazan university the activities in mathematical logic were also
executed by P.S.Proreckii, N.A.Vasiliev, N.N.Parfentiev. The first in
Russia course of lectures on mathematical logic also was read at
the Kazan university by professor Proreckii. However there were no stable
triditions in this field. It is possible to say about indirect eligibility
at formation of school of logic theory in Kazan State
University in 70th. The source of this eligibility was served
first of all by professor Morozov (1910-1975), scalene scientist
who had a high level of mathematical culture.
The researches
on logic theory at the Kazan university have deployed with full force in
second half of 70th, when from the isolated area it has turn into a speciality
of many young mathematicians. Increased concern to problems of logic
theory by young
mathematicians. Increased concern to problems of logic theory both
popularity of its ideas and methods could be explained, on the one
hand, by intensive development of computer science and programming, and
with other by infiltration of a postulational method into natural
mathematical sciences and cybernetics.
Main
role in quantitative increase and dilating
of subjects on mathematical logic researches at
the Kazan university has played the logical seminar under a
management
of M.M.Arslanov, schoolboy of V.V. Morozov. The seminar helped
to grow mathematicians, working in different areas of logic
theory and in miscellaneous cities of the USSR.
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