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.
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![\"\"](\"Edit_505d43e4-07c1-401c-b702-4e6a12c4d8f3.bmp\")
？were expressed as products of lines in near-linear
finite geometry ![\"\"](\"Edit_bcf23db7-eb33-4eef-964f-5fd9dff56542.bmp\")
？(where？p？is a prime). An
existence of lattice between any pair of near-linear finite geometry ![\"\"](\"Edit_83a2f977-e977-4b49-a2a1-da814ab8a3d3.bmp\")
？of ![\"\"](\"Edit_33501d40-7b81-4316-9e8f-257cf36ef567.bmp\")
？is confirmed. For ![\"\"](\"Edit_c1bf7e3b-4717-4c4f-91cc-59149bb4c43f.bmp\")
？of ![\"\"](\"Edit_183f7f9a-442a-4c5d-a18e-0d2c55743775.bmp\")
？and finite geometry ![\"\"](\"Edit_a2f388bb-1ea5-4b84-a186-4fae8dd0881b.bmp\")
？from the subsets of
the set 
