International Journal of Engineering Research in Electronics and Communication Engineering

SIGMA V Elements in Lattice Modules

Author : Dr. C. S. Manjarekar ¹ A. N. Chavan ² Dr. U. R. Biraje ³

Date of Publication :7th February 2017

Abstract: Let L be a compactly generated multiplicative lattice with 1 compact in which every finite product of compact elements is compact and M be a module over L which is also a compactly generated in which the largest element is compact. In this paper we define Ap, in the lattice module M and obtain many properties where p is prime element of L. Finally we define - element in a lattice module M and obtain it's properties

Reference :

1. D.D. Anderson, Abstract commutative ideal theory without chain condition, Algebra Universalis,6,(1976),131-145.
2. F. Alarcon, D.D. Anderson, C. Jayaram, Some results on abstrace commutative ideal theory, Periodica Mathemetica Hungerica, Vol 30 (1), (1995), pp.1-26.
3. F. Calliap and U. Tekir,Multiplication lattice modules, Iran. J. Sci. Technol, Trans. A. Sci.,35,(2011), 309-313.
4. R.P. Dilworth , Abstract Commutative Ideal theory, Paci_c. J. Math., 12,(1962)481-498
5. J. A.Johnson, ð›¼ -adic completions of Noetherian lattice modules, fund. math. ,66(3), (1970)347-373.
6. C. Jayaram , E. W. Johnson, ðœŽ- elements in multiplicative lattices, Czechoslovak Mathematical Journal, 48 (123)(1998).
7. C.S. Manjarekar and A.N. Chavan, Baer elements in lattice modules w.r.t. radical elements, IJORT, Volume 5, Issue 9, September-2016 [8] N. K. Thakre, C.S. Manjarekar and S. Maida, Abstract spectral theory II, Minimal characters and minimal spectrum of multiplicative lattices, Acta Sci. Math., 52 (1988) 53-67.
1. D.D. Anderson, Abstract commutative ideal theory without chain condition, Algebra Universalis,6,(1976),131-145.
2. F. Alarcon, D.D. Anderson, C. Jayaram, Some results on abstrace commutative ideal theory, Periodica Mathemetica Hungerica, Vol 30 (1), (1995), pp.1-26.
3. F. Calliap and U. Tekir,Multiplication lattice modules, Iran. J. Sci. Technol, Trans. A. Sci.,35,(2011), 309-313.
4. R.P. Dilworth , Abstract Commutative Ideal theory, Paci_c. J. Math., 12,(1962)481-498
5. J. A.Johnson, ð›¼ -adic completions of Noetherian lattice modules, fund. math. ,66(3), (1970)347-373.
6. C. Jayaram , E. W. Johnson, ðœŽ- elements in multiplicative lattices, Czechoslovak Mathematical Journal, 48 (123)(1998).
7. C.S. Manjarekar and A.N. Chavan, Baer elements in lattice modules w.r.t. radical elements, IJORT, Volume 5, Issue 9, September-2016 [8] N. K. Thakre, C.S. Manjarekar and S. Maida, Abstract spectral theory II, Minimal characters and minimal spectrum of multiplicative lattices, Acta Sci. Math., 52 (1988) 53-67.