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LINEARLY INDEPENDENT ELEMENTS IN N-GROUPS WITH FINITE GOLDIE DIMENSION
BHAVANARI SATYANARAYANA,KUNCHAM SYAM PRASAD Korean Mathematical Society 2005 대한수학회보 Vol.42 No.3
The concepts linearly independent elements and u-linearly independent elements in an N-group G where N is a near-ring, were introduced and studied. A few important results in the theory of vector spaces were generalized to N-groups.
ON FUZZY DIMENSION OF N-GROUPS WITH DCC ON IDEALS
Bhavanari, Satyanarayana,Kuncham, Syam Prasad,Tumurukota, Venkata Pradeep Kumar The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.2
In this paper we consider the fuzzy ideals of N-group G where N is a near-ring. We introduce the concepts: minimal elements, fuzzy linearly independent elements, and fuzzy basis of an N-group G and obtained fundamental related results.
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.
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.
Linearly independent elements in $N$-groups with finite Goldie dimension
Satyanarayana Bhavanari,Syam Prasad Kuncham 대한수학회 2005 대한수학회보 Vol.42 No.3
The concepts linearly independent elements and {itu-linearly independent elements} in an N-group G where Nis a near-ring, were introduced and studied. A few importantresults in the theory of vector spaces were generalized to N-groups.
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.
SOME RESULTS ON FUZZY COSETS AND HOMOMORPHISMS OF N-GROUPS
Satyanarayana, Bhavanari,Syam Prasad, Kuncaham,Venkata Pradeep Kumar, Tumurukora,Thota, Srinivas The Youngnam Mathematical Society Korea 2007 East Asian mathematical journal Vol.23 No.1
In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.