Author(s)

Semiu Oladipupo Oladejo¹, Adediran Dauda Adeshola², Adedayo David Adeniyi¹

¹Department of Mathematics, Faculty of Science, Gombe State University, Gombe, Nigeria.
²Department of Statistical and Mathematical Science, College of Pure and Applied Science, Kwara State University, Ilorin, Nigeria.

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 Z_q) of a finite quantum system ∏(d) with variables in Z_d and a finite system from the subsets of the set of divisors of d is established.

Lattice, Join, Meet, Least Upper Bound (LUB), Greatest Lower Bound (GLB), Partially Ordered Set (POSET)

Oladejo, S. , Adeshola, A. and Adeniyi, A. (2019) Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z_d. Journal of Quantum Information Science, 9, 111-121. doi: 10.4236/jqis.2019.92006.