半群关于自身的局部化

证明丰群A关于自身局部化A_A是其极大Abel群同态象,这时A的象集恰为A的极大可消半群象。还进一步证明,如果S为A的理想且为内区,则S关于S的局部化恰好等于A关于A的局部化。最后证明了交换逆半群关于幂等无半格的局部化同构于其关于本身的局部化。

LOCALIZATION OF A SEMIGROUP AT ITSELF

This paper proves that the localization A_A of a semigroup A at itself is the maximal abelian group homomorphism image of A. In this case, the image set of A is exactly the maximal camcellation semigroup image of A. Furthermore, the paper proves that if S is an ideal and an inner domain in A, then the localization of S at S is exactly equal to the localization of A at A. Finally, in this paper, it is implied that the localization of a commutative inverse semigroup at the semilattice of its idempotents is isomorphic to the localization of the semigroup at itself.