An interesting topic in the ring theory is the classification of finite rings. Although rings of certain orders have already been classified, a full description of all rings of a given order remains unknown. The purpose of this paper is to classify all finite rings (up to isomorphism) of a given order. In doing so, we introduce a new concept of quasi basis for certain type of modules, which is a useful computational tool for dealing with finite rings. Then, using this concept, we give structure and isomorphism theorems for finite rings and state our main result to classify (up to isomorphism) the finite rings of a given order. Finally, based on these results, we describe an algorithm to calculate the structure of all such rings. We have implemented our new algorithm in Maple, and we apply it to an example.
Based on a systematic study of Polish sociological literature produced in the period stretching between the elevation of Władysław Gomułka to the post of the Party's first secretary in October 1956 to the first free elections in Poland in June 1989, the author of this article offers an account of the main dilemmas and the varieties of pluralism in Polish sociology during the state socialist era. The author claims that, with the exception of the Stalinist period, Polish sociologists always occupied diverse positions on 'government' and 'society', but this diversity yielded to change in response to a particular time. Generally, in 1956-1989 Polish sociology was something unique in comparison with sociology in other so-called people's democracies, as it had a considerably high status in the country and in the world, including the West. The author argues that Polish sociology did not have to undergo a revolution in 1989 and make the move from Marxist to bourgeois sociology, as since 1956 (or even earlier, since 1945) it had been undergoing continuous change and constant reform (in theoretical domain and concerning its division into sub-disciplines) and maintained a consistent level of diversity in various respects.