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Zero Divisor Graph of a Poset with Respect to an Ideal
  • V. Joshi
  • Mathematics, Computer Science
  • Order
  • 1 November 2012
The zero divisor graph GI(P) of a poset P (with 0) with respect to an ideal I is introduced and proves a form of Beck’s conjecture for posets with 0. Expand
Order-free integers (mod m)
For a fixed natural number m, an integer t is said to possess weak order (mod m), if there exists a natural number n satisfying tn+1≡t (mod m); and t is said to be order-free (mod m) otherwise.
Characterizations of Standard Elements in Posets
The fundamental characterization theorem of standard elements in lattices is extended to posets and several other characterizations ofstandard elements are obtained in an atomistic, dually sectionally semi-complemented poset. Expand
Characterizations of 0-distributive posets
The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that everyExpand
The zero divisor graphs of Boolean posets
In this paper, it is proved that if B is a Boolean poset and S is a bounded pseudocomplemented poset such that S\Z(S) = {1}, then Γ(B) ≌ Γ(S) if and only if B ≌ S. Further, we characterize the graphsExpand
The Graph of Equivalence Classes of Zero Divisors
We introduce a graph of equivalence classes of zero divisors of a meet semilattice with 0. The set of vertices of are the equivalence classes of nonzero zero divisors of and two vertices and areExpand
On the zero divisor graphs of p m-lattices
The diameter and the eccentricity of Γ ( L ) when L is a semiprimitive p m -lattice L is characterized and an algebraic and a topological characterization is given for the graph Γ(L) to be triangulated or hyper-triangulated. Expand
In this paper, we introduce the concepts of primal and weakly primal ideals in lattices. Further, the diameter of the zero divisor graph of a lattice with respect to a non-primal ideal is determined.
Prime ideals in 0-distributive posets
In the first section of this paper, we prove an analogue of Stone’s Theorem for posets satisfying DCC by using semiprime ideals. We also prove the existence of prime ideals in atomic posets in whichExpand
On n-normal posets
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 andExpand