Cent. Eur. J. Math. • 8(5) • 2010 • 985-991 DOI: 10.2478/s11533-010-0062-z Central European Journal of Mathematics On n-normal posets Research Article Radomír Halaš 1 ∗ , Vinayak Joshi 2 † , Vilas S. Kharat 2 ‡ 1 Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, Olomouc, Czech Republic 2 Department of Mathematics, University of Pune, Pune, India Received 4 August 2009; accepted 12 August 2010 Abstract: A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained. MSC: 06A11, 06B10, 06D75 Keywords: n-normal poset • Distributive poset • Prime ideal • Unique minimal prime ideal • Polar © Versita Sp. z o.o. 1. Introduction A distributive lattice is called normal, if its every prime ideal contains a unique minimal prime ideal. These lattices were studied e.g. by Cornish [1], Zaanen [13], Pawar [12] and others. Grätzer and Schmidt [4] described Stone lattices as distributive pseudocomplemented lattices in which every prime ideal contains a unique minimal prime ideal. Another notion of a normal lattice can be found in Johnstone [8]. Later on, Lee [10] generalized the results of Grätzer and Schmidt [4] by considering lattices each prime ideal of which contains at most n minimal prime ones. Cornish [2] called such lattices n-normal lattices and gave some of their characterizations. The concept of n-normality for distributive semilattices was considered by Nimbhorkar and Wasadikar [11]. The aim of this paper is to introduce and characterize n-normality in a more general setting, namely for partially ordered sets. In fact, we have generalized the main results of Cornish [2] and Nimbhorkar and Wasadikar [11] for finite posets. ∗ E-mail: Halas@inf.upol.cz † E-mail: vvj@math.unipune.ac.in ‡ E-mail: vsk@math.unipune.ac.in 985