| Abstract:
A multiplicative semilattce is an algebra
<C; ·,v,0>
such that
- <C; v,0> is a join
semilattice with zero
( x v x = x; x v y = y v x; x v (y
v z) = (x v y) v z; x v 0 = x ),
- <C; ·,0>
is a commutative semigroup with zero
( x · y =
y · x; x · (y · z) =
(x · y) · z; x · 0 = 0 ),
- multiplication distributes over join
( x · (y v z) = (x · y) v (x · z) ).
The canonical example is the set of
finitely generated ideals of a commutative ring with 1, where
"v"
is ideal sum and "·" is ideal product. This will be an expository
talk on these algebras and their relation to ideal theory for
commutative rings.
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