Journal Article10.2478/S11533-010-0062-Z
On n-normal posets
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TL;DR: In this paper, the authors used the prime ideal theorem for finite ideal distributive posets and obtained properties and characterizations of n-normal posets, where every prime ideal contains at most n minimal prime ideals.
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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.
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Citations
n -Normal residuated lattices
Saeed Rasouli,Michiro Kondo +1 more
- 01 Jan 2020
TL;DR: In this article, the notion of n-normal residuated lattices was introduced and investigated, in which every prime filter contains at most n minimal prime filters and the set of coannulets is a sublattice.
Prime ideals in 0-distributive posets
Vinayak Joshi,Nilesh Mundlik +1 more
TL;DR: In this paper, it was shown that every maximal non-dense (non-principal) ideal of a 0-distributive poset (meet-semilattice) is prime.
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Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures
Jun Yan,Qianqian Sui,Zhirui Fan,Zunyi Duan +3 more
- 01 Jan 2022
TL;DR: In this paper , a multiscale and multi-material topology optimization model for thermoelastic lattice structures (TLSs) considering mechanical and thermal loading based on the Extended Multiscale Finite Element Method (EMsFEM) was established with minimizing strain energy and structural mass as the objective function and constraint, respectively.
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The hull-kernel topology on prime ideals in posets
Nilesh Mundlik,Vinayak Joshi,Radomír Halaš +2 more
- 01 Apr 2017
TL;DR: A characterization of a space of maximal ideals of a poset to be a normal space is proved.
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Baer ideals in 0-distributive posets
Vinayak Joshi,Nilesh Mundlik +1 more
TL;DR: Pawar et al. as discussed by the authors studied Baer ideals in posets and obtained some characterizations of Baer ideal in 0-distributive posets, and showed that every ideal is Baer (normal) if and only if every prime ideal is normal.
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References
On a problem of M. H. Stone
G. Grätzer,E. T. Schmidt +1 more
TL;DR: In this paper, the authors considered the distributive pseudo-complemented lattices in which a*u a**= 1 holds for all a as an immediate generalization of the Boolean algebras.
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$n$-normal lattices
William H. Cornish
- 01 Jan 1974
TL;DR: In this article, it was shown that a distributive lattice L with 0 is relatively n-normal if and only if for any (x 2 x, x e L such that x Ax. = O for any ij i,j 0, n,(xV (x]V... V(xn] =L, 2) for any n + 1 incomparable prime ideals P0, P1,..., Pn, P0V P1 V...VP = L. n
Semiprime Ideals and Separation Theorems for Posets
Vilas Kharat,Khalid A. Mokbel +1 more
TL;DR: A generalization of Stone’s Separation Theorem for posets is obtained in respect of prime ideals in relation to semiprime ideals of a poset.
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