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| On the Dimension of the Quotient Ring R/K Where K is a Complement
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Source |
International Journal of Contemporary Advanced Mathematics (IJCM) |
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Volume: 1 Issue: 2 |
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Pages: NULL |
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Publication
Date: January / February |
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ISSN
(Online): 1985 |
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Pages |
16 - 22 |
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Published
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08-02-2011 |
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Publisher |
CSC
Journals, Kuala Lumpur,
Malaysia |
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KEYWORDS: Collision, Risk, Inland Waterways, Environmental Prevention |
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| The aim of the present paper is to obtain some interesting results related to the concept “finite dimension” in the theory of associative rings R with respect to two sided ideals. It is known that if an ideal H of R has finite dimension, then there exist uniform ideals Ui, 1 i n of R such that the sum U1 U2 … Un is essential in H. This n is independent of choice of uniform ideals and we call it as dimension of H (we write dim H, in short). We obtain some important relations between the concepts complement ideals and essential ideals. Finally, we proved that dim(R/K) = dim R – dim K for a complement ideal K of R. We include some necessary examples. |
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| 1 |
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| 2 |
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| 3 |
Bh. Satyanarayana and Sk. Mohiddin Shaw “Fuzzy Dimension of Modules over Rings (Monograph)”, VDM Verlag Dr Muller, Germany, (2010) (ISBN: 978-3-639-23197-7).
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Bh. Satyanarayana D. Nagaraju, K. S. Balamurugan and L. Godloza “Finite Dimension in Associative Rings”, Kyungpook Mathematical Journal, 48:37-43, 2008.
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Bh. Satyanarayna, D. Nagaraju, L. Godloza and S. Sreenadh “Some Dimension Conditions in Rings with Finite Dimension”, The PMU Journal of Humanities and Sciences 1(1):69-75, 2010.
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Bh. Satyanarayana, D. Nagaraju, Sk. Mohiddin Shaw and S. Eswaraiah Setty “E-irreducible Ideals and Some Equivalent Conditions”, Proceedings of International Conference on Challenges and Applications of Mathematics in Science and Technology (CAMIST), NIT, Rourkela, India, January 11-13, 2010, PP 681-687, Macmillan Advanced Research Series, New Delhi, 2010 (ISBN: 978-0230-32875-4).
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Bh. Satyanarayana, L. Godloza and D. Nagaraju “Ideals and Direct Product of Zero Square Rings”, East Asian Mathematical Journal 24:377-387, 2008.
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Bh. Satyanarayana and K. Syam Prasad “Discrete Mathematics and Graph Theory” Prentice Hall of India, New Delhi, (2009) (ISBN: 978-81-203-3842-5).
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| Satyanarayana Bhavanari : Colleagues
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| Nagaraju Dasari : Colleagues
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| Babu Prasad Munagala : Colleagues
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| Mohiddin Shaw Shaik : Colleagues
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