%0 Journal Article %T Lattice Theory for Finite Dimensional Hilbert Space with Variables in Zd %A Semiu Oladipupo Oladejo %A Adediran Dauda Adeshola %A Adedayo David Adeniyi %J Journal of Quantum Information Science %P 111-121 %@ 2162-576X %D 2019 %I Scientific Research Publishing %R 10.4236/jqis.2019.92006 %X In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry $\"\"$ were expressed as products of lines in near-linear finite geometry $\"\"$ (where p is a prime). An existence of lattice between any pair of near-linear finite geometry $\"\"$ of $\"\"$ is confirmed. For q|d, a one-to-one correspondence between the set of subgeometry $\"\"$ of $\"\"$ and finite geometry $\"\"$ from the subsets of the set {D(d)} of divisors of d (where each divisor represents a finite geometry) and set of subsystems {∏(q)} (with variables in Zq) of a finite quantum system ∏(d) with variables in Zd and a finite system from the subsets of the set of divisors of d is established. %K Lattice %K Join %K Meet %K Least Upper Bound (LUB) %K Greatest Lower Bound (GLB) %K Partially Ordered Set (POSET) %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=91855