Gallery of Lattices of Ideals of B(n,i)

Lattice of Ideals of a Finite Semiring
 
Content:
 
B(2,i)
B(3,i)
B(4,i)
B(5,i)
B(6,i)
B(7,i)
B(8,i)
B(9,i)
B(10,i)
Other

 		  
 
Below you will find a collection of lattices of ideals of B(n,i). Click on the 2D graph to view it in 3D (you will need a VRML browser).

  
B(2,0)
Ideals: {0}, {0,1}
[Graphics:gallerygr3.gif]
  
B(2,1)
Ideals: {0}, {0,1}
[Graphics:gallerygr5.gif]



 
   

B(3,0)
Ideals: {0}, (0,1,2)
[Graphics:gallerygr7.gif]



 
   

B(3,1)
Ideals:{0},{0,2},{0,1,2}
[Graphics:gallerygr9.gif]



 
   

B(3,2)
Ideals: {0},{0,2},{0,1,2}
[Graphics:gallerygr11.gif]



 
   

B(4,0)
Ideals:{0},{0,2},{0,1,2,3}
[Graphics:gallerygr13.gif]



 
   

B(4,1)
Ideals: {0},{0,3},{0,1,2,3}
[Graphics:gallerygr15.gif]



 
   

B(4,2)
Ideals: {0},{0,2},{0,2,3},{0,1,2,3}
[Graphics:gallerygr17.gif]



 
   

B(4,3)
Ideals: {0},{0,3},{0,2,3},{0,1,2,3}
[Graphics:gallerygr19.gif]



 
   

B(5,0)
Ideals: {0},{0,1,2,3,4}
[Graphics:gallerygr21.gif]



 
   

B(5,1)
Ideals:{0},{0,4},{0,2,4},{0,1,2,3,4}
[Graphics:gallerygr23.gif]



 
   

B(5,2)
Ideals:{0},{0,3},{0,2,3,4},{0,1,2,3,4}
[Graphics:gallerygr25.gif]



 
   

B(5,3)
Ideals:{0},{0,3},{0,2,3,4},{0,1,2,3,4}
[Graphics:gallerygr27.gif]



 
   

B(5,4)
Ideals:{0},{0,4},{0,2,4},{0,3,4},{0,2,3,4},{0,1,2,3,4}
[Graphics:gallerygr29.gif]



 
   

B(6,0)
Ideals:{0},{0,3},{0,2,4},{0,1,2,3,4,5}
[Graphics:gallerygr31.gif]



 
   

B(6,1)
Ideals:{0},{0,5},{0,1,2,3,4,5}
[Graphics:gallerygr33.gif]



 
   

B(6,2)
Ideals:{0},{0,4},{0,2,4},{0,2,3,4,5},{0,1,2,3,4,5}
[Graphics:gallerygr35.gif]



 
   

B(6,3)
Ideals:{0},{0,3},{0,3,4,5},{0,2,3,4,5},{0,1,2,3,4,5}
[Graphics:gallerygr37.gif]



 
   

B(6,4)
Ideals:{0},{0,4},{0,2,4},{0,4,5},{0,2,4,5},{0,3,4,5},{0,2,3,4,5},{0,1,2,3,4,5}
[Graphics:gallerygr39.gif]



 
   

B(6,5)
Ideals:{0},{0,5},{0,3,5},{0,4,5},{0,2,4,5},{0,3,4,5},{0,2,3,4,5},{0,1,2,3,4,5}
[Graphics:gallerygr41.gif]



 
   

B(7,0)
Ideals:{0},{0,1,2,3,4,5,6}
[Graphics:gallerygr43.gif]


  

B(7,1)
Ideals:{0},{0,6},{0,3,6},{0,2,4,6},{0,1,2,3,4,5,6}
[Graphics:gallerygr45.gif]


  

B(7,2)
Ideals:{0},{0,5},{0,2,3,4,5,6},{0,1,2,3,4,5,6}
[Graphics:gallerygr47.gif]


  

B(7,3)
Ideals:{0},{0,4},{0,4,6},{0,2,4,6},{0,3,4,5,6},{0,2,3,4,5,6},{0,1,2,3,4,5,6}
[Graphics:gallerygr49.gif]


  

B(7,4)
Ideals:{0},{0,6},{0,3,6},{0,4,5,6},{0,2,4,5,6},{0,3,4,5,6},{0,2,3,4,5,6},
{0,1,2,3,4,5,6}
[Graphics:gallerygr51.gif]


  

B(7,5)
Ideals:{0},{0,6},{0,4,6},{0,5,6},{0,2,4,6},{0,3,5,6},{0,4,5,6},{0,2,4,5,6},
{0,3,4,5,6},{0,2,3,4,5,6},{0,1,2,3,4,5,6}
[Graphics:gallerygr53.gif]


  

B(7,6)
Ideals:{0},{0,6},{0,3,6},{0,4,6},{0,5,6},{0,2,4,6},{0,3,4,6},{0,3,5,6},
{0,4,5,6},{0,2,4,5,6},{0,3,4,5,6},{0,2,3,4,5,6},{0,1,2,3,4,5,6}
[Graphics:gallerygr55.gif]


  

B(8,0)
Ideals:{0},{0,4},{0,2,4,6},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr57.gif]


  

B(8,1)
Ideals:{0},{0,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr59.gif]


  

B(8,2)
Ideals:{0},{0,6},{0,3,6},{0,2,4,6},{0,2,3,4,5,6,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr61.gif]


  

B(8,3)
Ideals:{0},{0,5},{0,3,4,5,6,7},{0,2,3,4,5,6,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr63.gif]


  

B(8,4)
Ideals:{0},{0,4},{0,4,6},{0,2,4,6},{0,4,5,6,7},{0,2,4,5,6,7},{0,3,4,5,6,7},
{0,2,3,4,5,6,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr65.gif]


  

B(8,5)
Ideals:{0},{0,6},{0,3,6},{0,5,6,7},{0,3,5,6,7},{0,4,5,6,7},{0,2,4,5,6,7},
{0,3,4,5,6,7},{0,2,3,4,5,6,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr67.gif]


  

B(8,6)
Ideals:{0},{0,6},{0,4,6},{0,6,7},{0,2,4,6},{0,3,6,7},{0,4,6,7},{0,5,6,7},
{0,2,4,6,7},{0,3,4,6,7},{0,3,5,6,7},{0,4,5,6,7},{0,2,4,5,6,7},{0,3,4,5,6,7},
{0,2,3,4,5,6,7},{0,1,2,3,4,5,6,7}
[Graphics:gallerygr69.gif]


  

B(8,7)
Ideals:{0},{0,7},{0,4,7},{0,5,7},{0,6,7},{0,3,6,7},{0,4,5,7},{0,4,6,7},{0,5,6,7},
{0,2,4,6,7},{0,3,4,6,7},{0,3,5,6,7},{0,4,5,6,7},{0,2,4,5,6,7},{0,3,4,5,6,7},
{0,2,3,4,5,6,7}, {0,1,2,3,4,5,6,7}
[Graphics:gallerygr71.gif]


  

B(9,0)
Ideals:{0},{0,3,6},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr73.gif]


  

B(9,1)
Ideals:{0},{0,8},{0,4,8},{0,2,4,6,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr75.gif]


  

B(9,2)
Ideals:{0},{0,7},{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr77.gif]


  

B(9,3)
Ideals:{0},{0,6},{0,3,6},{0,4,6,8},{0,2,4,6,8},{0,3,4,5,6,7,8},
{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr79.gif]


  

B(9,4)
Ideals:{0},{0,5},{0,4,5,6,7,8},{0,2,4,5,6,7,8},{0,3,4,5,6,7,8},
{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr81.gif]


  

B(9,5)
Ideals:{0},{0,8},{0,4,8},{0,6,8},{0,4,6,8},{0,2,4,6,8},{0,5,6,7,8},
{0,3,5,6,7,8},{0,4,5,6,7,8},{0,2,4,5,6,7,8},{0,3,4,5,6,7,8},{0,2,3,4,5,6,7,8},
{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr83.gif]


  

B(9,6)
Ideals:{0},{0,6},{0,3,6},{0,6,7,8},{0,3,6,7,8},{0,4,6,7,8},{0,5,6,7,8},
{0,2,4,6,7,8},{0,3,4,6,7,8},{0,3,5,6,7,8},{0,4,5,6,7,8},{0,2,4,5,6,7,8},
{0,3,4,5,6,7,8},{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr85.gif]


  

B(9,7)
Ideals:{0},{0,8},{0,4,8},{0,6,8},{0,7,8},{0,4,6,8},{0,4,7,8},{0,5,7,8},
{0,6,7,8},{0,2,4,6,8},{0,3,6,7,8},{0,4,5,7,8},{0,4,6,7,8},{0,5,6,7,8},
{0,2,4,6,7,8},{0,3,4,6,7,8},{0,3,5,6,7,8},{0,4,5,6,7,8},{0,2,4,5,6,7,8},
{0,3,4,5,6,7,8},{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr87.gif]


  

B(9,8)
Ideals:{0},{0,8},{0,4,8},{0,5,8},{0,6,8},{0,7,8},{0,3,6,8},{0,4,5,8},
{0,4,6,8},{0,4,7,8},{0,5,6,8},{0,5,7,8},{0,6,7,8},{0,2,4,6,8},{0,3,5,6,8},
{0,3,6,7,8},{0,4,5,6,8},{0,4,5,7,8},{0,4,6,7,8},{0,5,6,7,8},{0,2,4,6,7,8},
{0,3,4,6,7,8},{0,3,5,6,7,8},{0,4,5,6,7,8},{0,2,4,5,6,7,8},{0,3,4,5,6,7,8},
{0,2,3,4,5,6,7,8},{0,1,2,3,4,5,6,7,8}
[Graphics:gallerygr89.gif]


  

B(10,0)
Ideals:{0},{0,5},{0,2,4,6,8},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr91.gif]


  

B(10,1)
Ideals:{0},{0,9},{0,3,6,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr93.gif]


  

B(10,2)
Ideals:{0},{0,8},{0,4,8},{0,2,4,6,8},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr95.gif]


  

B(10,3)
Ideals:{0},{0,7},{0,3,4,5,6,7,8,9},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr97.gif]
  
B(10,4)
Ideals:{0},{0,6},{0,6,9},{0,3,6,9},{0,4,6,8},{0,2,4,6,8},{0,4,5,6,7,8,9},
{0,2,4,5,6,7,8,9},{0,3,4,5,6,7,8,9},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr99.gif]
  
B(10,5)
Ideals:{0},{0,5},{0,5,6,7,8,9},{0,3,5,6,7,8,9},{0,4,5,6,7,8,9},
{0,2,4,5,6,7,8,9},{0,3,4,5,6,7,8,9},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr101.gif]


  

B(10,6)
Ideals:{0},{0,8},{0,4,8},{0,6,8},{0,4,6,8},{0,2,4,6,8},{0,6,7,8,9},
{0,3,6,7,8,9},{0,4,6,7,8,9},{0,5,6,7,8,9},{0,2,4,6,7,8,9},{0,3,4,6,7,8,9},
{0,3,5,6,7,8,9},{0,4,5,6,7,8,9},{0,2,4,5,6,7,8,9},{0,3,4,5,6,7,8,9},
{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr103.gif]


  

B(10,7)
Ideals:{0},{0,9},{0,6,9},{0,3,6,9},{0,7,8,9},{0,4,7,8,9},{0,5,7,8,9},
{0,6,7,8,9},{0,3,6,7,8,9},{0,4,5,7,8,9},{0,4,6,7,8,9},{0,5,6,7,8,9},
{0,2,4,6,7,8,9},{0,3,4,6,7,8,9},{0,3,5,6,7,8,9},{0,4,5,6,7,8,9},
{0,2,4,5,6,7,8,9},{0,3,4,5,6,7,8,9},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr105.gif]


  

B(10,8)
Ideals:{0},{0,8},{0,4,8},{0,6,8},{0,8,9},{0,4,6,8},{0,4,8,9},{0,5,8,9},
{0,6,8,9},{0,7,8,9},{0,2,4,6,8},{0,3,6,8,9},{0,4,5,8,9},{0,4,6,8,9},{0,4,7,8,9},
{0,5,6,8,9},{0,5,7,8,9},{0,6,7,8,9},{0,2,4,6,8,9},{0,3,5,6,8,9},{0,3,6,7,8,9},
{0,4,5,6,8,9},{0,4,5,7,8,9},{0,4,6,7,8,9},{0,5,6,7,8,9},{0,2,4,6,7,8,9},
{0,3,4,6,7,8,9},{0,3,5,6,7,8,9},{0,4,5,6,7,8,9},{0,2,4,5,6,7,8,9},
{0,3,4,5,6,7,8,9},{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr107.gif]


  

B(10,9)
Ideals:{0},{0,9},{0,5,9},{0,6,9},{0,7,9},{0,8,9},{0,3,6,9},{0,4,8,9},
{0,5,6,9},{0,5,7,9},{0,5,8,9},{0,6,7,9},{0,6,8,9},{0,7,8,9},{0,3,6,7,9},
{0,3,6,8,9},{0,4,5,8,9},{0,4,6,8,9},{0,4,7,8,9},{0,5,6,7,9},{0,5,6,8,9},{0,5,7,8,9},
{0,6,7,8,9},{0,2,4,6,8,9},{0,3,5,6,8,9},{0,3,6,7,8,9},{0,4,5,6,8,9},
{0,4,5,7,8,9},{0,4,6,7,8,9},{0,5,6,7,8,9},{0,2,4,6,7,8,9},{0,3,4,6,7,8,9},
{0,3,5,6,7,8,9},{0,4,5,6,7,8,9},{0,2,4,5,6,7,8,9},{0,3,4,5,6,7,8,9},
{0,2,3,4,5,6,7,8,9},{0,1,2,3,4,5,6,7,8,9}
[Graphics:gallerygr109.gif]