Abstract
A common generalization of different notions of ideals met in literature together with the associated notions of distributivity in ordered sets are studied. A restricted prime ideal theorem is proved. Moreover, a new characterization of algebraic topped intersection structures is presented.
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References
Abian, A., Amin, W. A.,Existence of prime ideals and ultrafilters in partially ordered sets, Czech. Math. J.,40 1990, 159–163.
Davey, B. A., Priestley, H. A.,Introduction to Lattices and Order, Cambridge University Press 1990.
Doyle, W.,An arithmetical theorem for partially ordered sets, Bull. Amer. Math. Soc.,56 1950, 366.
Frink, O.,Ideals in partially ordered sets, Amer. Math. Monthly,61 1954, 223–234.
Halaš, R., Rachůnek, J.,Polars and prime ideals in ordered sets, Discuss. Math., Algebra Stoch. Methods,15 1995, 43–59.
Niederle, J.,Boolean and distributive ordered sets: characterization and representation by sets, Order,12 1995, 189–210.
Venkatanarasimhan, P. V.,Pseudo-complements in posets, Proc. Amer. Math. Soc.,28 1971, 9–17.
Wright, J. B., Wagner, E. G., Thatcher, J. W.,A uniform approach to inductive posets and inductive closure, Theoret. Comput. Sci., 7 1978, 57–77.
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Niederle, J. Ideals in ordered sets, a unifying approach. Rend. Circ. Mat. Palermo 55, 287–295 (2006). https://doi.org/10.1007/BF02874708
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DOI: https://doi.org/10.1007/BF02874708
Keywords
- Algebraic topped intersection structure
- ideal
- pseudoideal
- Frink ideal
- Doyle pseudoideal
- S-ideal
- primeS-ideal
- S-distributive ordered set
- primeS-ideal theorem