Filters of Coz(X) | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 8، دوره 7، Special Issue on the Occasion of Banaschewski's 90th Birthday (II) - شماره پیاپی 1، مهر 2017، صفحه 107-123 اصل مقاله (954.69 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Papiya Bhattacharjee* 1؛ Kevin M. Drees2 | ||
| 1School of Science, Penn State Behrend, Erie, PA 16563, USA. | ||
| 2Department of Mathematics and Information Technology, Mercyhurst University, Erie PA. | ||
| چکیده | ||
| In this article we investigate filters of cozero sets for real-valued continuous functions, called $coz$-filters. Much is known for $z$-ultrafilters and their correspondence with maximal ideals of $C(X)$. Similarly, a correspondence will be established between $coz$-ultrafilters and minimal prime ideals of $C(X)$. We will further notice various properties of $coz$-ultrafilters in relation to $P$-spaces and $F$-spaces. In the last two sections, the collection of $coz$-ultrafilters will be topologized, and then compared to the hull-kernel and the inverse topologies placed on the collection of minimal prime ideals of $C(X)$ and general lattice-ordered groups. | ||
تازه های تحقیق | ||
Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday | ||
| کلیدواژهها | ||
| Cozero sets؛ ultrafilters؛ minimal prime ideals؛ $P$-space؛ $F$-space؛ inverse topology؛ $ell$-groups | ||
| مراجع | ||
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[1] Atiyah, M. and MacDonald, I., "Introduction to Commutative Algebra", Addison-Wesley Publishing Co., 1969. [2] Bhattacharjee, P. and McGovern, W., Lamron `-groups, in preparation, 2017. [3] Bhattacharjee, P. and McGovern, W., When Min(A)1 is Hausdorf, Comm. Algebra 41(1) (2013), 99-108. [4] Brooks, R., On Wallman compactification, Fund. Math. 60 (1967), 157-173. [5] Conrad, P. and Martinez, J., Complemented lattice-ordered groups, Indag. Math. (N.S.) 1(3) (1990), 281-297. [6] Darnel, M., "Theory of Lattice-Ordered Groups", Marcel Dekker, 1995. [7] Dashiell, F., Hager, A., and Henriksen, M., Order-Cauchy completions of rings and vector lattices of continuous functions, Canad. J. Math XXXII(3) (1980), 657-685. [8] Engelking, R., "General Topology", Helderman Verlag, 1989. [9] Fine, N., Gilman, L., and Lambek, J., "Rings of Quotients of Rings of Functions", McGill University Press, 1966. [10] Gillman, L. and Henriksen, M., Rings of continuous functions in which every finitely generated ideal is principal, Trans. Amer. Math. Soc. 82(2) (1956), 366-391. [11] Gillman, L. and Jerison, M., "Rings of Continuous Functions", D. Van Nostrand Co., 1960. [12] Henriksen, M. and Jerison, M., The space of minimal prime ideals of a commutative ring, Trans. Amer. Math. Soc. 115 (1965), 110-130. [13] Huckaba, J., Commutative Rings with Zero Divisors, Marcel Dekker, 1988. [14] Kaplansky, I., "Commutative Rings (Revised ed.)", University of Chicago Press, 1974. [15] Knox, M., Levy, R., McGovern, W., and Shapiro, J., Generalizations of complemented rings with applications to rings of functions, J. Algebra Appl. 7(6) (2008), 1-24. [16] Lang, S., "Algebra", Springer, 2002. [17] McGovern, W., Neat rings, J. Pure Appl. Algebra 205(2) (2006), 243-265. [18] Samuel, P., Ultrafilters and compactification of uniform spaces, Trans. Amer. Math. Soc. 64 (1948), 100-132. [19] Wallman, H., Lattice and topological spaces, Ann. of Math. 39(2) (1938), 112-126. | ||
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