Bourbaki

Exercise 16, § 1

Algebra, VI, p. 32

Show that

n⋅inf⁡(x,y)+inf⁡(nx,ny)=2n⋅inf⁡(x,y) n \cdot \inf(x, y) + \inf(nx, ny) = 2n \cdot \inf(x, y)

in a semi-lattice ordered monoid (cf. Ex. 8). Deduce that inf⁡(nx,ny)=n⋅inf⁡(x,y)\inf(nx, ny) = n \cdot \inf(x, y) if inf⁡(x,y)\inf(x, y) is a regular element.

Solution

No solution has been written yet.

Transcribed from the printed volume. Not translated.