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.