http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
IDEALS AND DIRECT PRODUCT OF ZERO SQUARE RINGS
Bhavanari, Satyanarayana,Lungisile, Goldoza,Dasari, Nagaraju The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.4
We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.
Ideals and direct product of zero square rings
Satyanarayana Bhavanari,Goldoza Lungisile,Nagaraju Dasari 영남수학회 2008 East Asian mathematical journal Vol.24 No.4
We consider associative ring R (not necessarily commutative). In this paper the concepts: zero square ring of type-1/type-2, zero square ideal of type-1/type-2, zero square dimension of a ring R were introduced and obtained several important results. Finally, some relations between the zero square dimension of the direct sum of finite number of rings; and the sum of the zero square dimension of individual rings; were obtained. Necessary examples were provided.
Finite Dimension in Associative Rings
Bhavanari, Satyanarayana,Dasari, Nagaraju,Subramanyam, Balamurugan Kuppareddy,Lungisile, Godloza Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.1
The aim of the present paper is to introduce the concept "Finite dimension" in the theory of associative rings R with respect to two sided ideals. We obtain that if R has finite dimension on two sided ideals, then there exist uniform ideals $U_1,U_2,\ldots,U_n$ of R whose sum is direct and essential in R. The number n is independent of the choice of the uniform ideals $U_i$ and 'n' is called the dimension of R.