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ON PROJECTIVE L- MODULES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 3، دوره 2، شماره 1، تیر 2005، صفحه 19-28 اصل مقاله (287.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2005.472 | ||
| نویسنده | ||
| PAUL ISAAC | ||
| DEPARTMENT OF MATHEMATICS, BHARATA MATA COLLEGE, THRIKKAKARA KOCHI - 682 021, KERALA, INDIA | ||
| چکیده | ||
| The concepts of free modules, projective modules, injective modules and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper we give an alternate definition for projective L-modules. We prove that every free L-module is a projective L-module. Also we prove that if μ∈L(P) is a projective L-module, and if 0→η f→ ν g→ μ →0 is a short exact sequence of L-modules then η⊕ μ >ν. Further it is proved that if μ∈L(P) is a projective L-module then μ is a fuzzy direct summand of a free L-module. | ||
| کلیدواژهها | ||
| The concepts of free modules؛ projective modules | ||
| مراجع | ||
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[1] G. Birkhoff, Lattice theory, Ameri. Math. Soci. Coll. Pub (1967). [2] K. R. Goodearl and R. B. Warfield, Jr., An introduction to noncommutative Noetherian rings, Cambridge University Press (1989). [3] T. W. Hungerford, Algebra, Springer-Verlag (1974). [4] P. Isaac, On L-modules, Proceedings of the National Conference on Mathematical Modeling, March 14-16, (2002); Baselius College, Kottayam, Kerala, India, 123-134. [5] P. Isaac, Simple and Semisimple L-modules (to appear in The Journal of Fuzzy Math.). [6] P. Isaac, Exact sequences of L-modules (communicated). [7] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific (1998). [8] G. C. Muganda, Free fuzzy modules and their bases, Inform. Sci.,72 (1993) 65-82. [9] F. Pan, Fuzzy finitely generated modules, Fuzzy Sets and Systems, 21 (1987) 105-113. [10] A. Rosenfeld, Fuzzy groups, Journal Math. Anal. Appl. 35 (1971) 512-517. [11] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965) 338-353. [12] M. M. Zahedi and A. Ameri, On fuzzy projective and injective modules, Journal Fuzzy. Math.3, No.1 (1995) 181-190. [13] M. M. Zahedi, Some results on L-fuzzy modules, Fuzzy Sets and Systems, 55 (1993) 355-361. | ||
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