THE LATTICE OF ALL SEMI-SIMPLE CLASSES OF RINGS
DOI:
https://doi.org/10.53808/KUS.2001.3.2.0136-seKeywords:
Lattice, Radical, Semi-simpleAbstract
The collection of all radicals of an associative ring is a lattice under the natural ordering of radicals. This lattice has been studied by Leavitt and Snider. In this paper it has been shown that the collection of all semi-simple classes of associative rings too is a lattice Ls under the natural ordering. The properties of this radical and its relation with the lattice of all radicals have been studied. A structure theorem has been established.
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References
Divinisky, N.J. 1965. Rings and Radicals. University of Toronto Press, Toronto, pp. 4-150.
Gratzer, G.1971. Lattice Theory; First Concepts and Distributive Lattices. W.H. Freeman & Co., San Fransisco,. pp. 100-112
Leavitt, W.G.1967. Sets of radical classes, Publ. Math. Debrecen, 14: 321-324.
Rutherford, D.E. 1965. Introduction to Lattice Theory. Oliver & Boyd, London, pp. 135-148.
Snider, R .L.1972. Lattices of Radicals, Pacific Journal of Mathematics. Vol. 40, No. l , pp. 207-220.
Wiegandt, R.1983. Radical Theory of Rings: The Mathematics Student. Vol. 51 No. 1-4, pp. 145-185.
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Copyright (c) 2001 Khulna University Studies
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