Estructura de los PLARI-Semigrupos

Abstract

In the following work consist in create a structure for the primitive left ample semigroups. For this, it is necessary to consider the extent of Green relationships $ \mathcal{R}^*, \mathcal{L}^* $ between others. Remember that a semigroup is set with inner operation $ \cdot $ such as for all $ x, y, z \in S $ we have, $ (x \cdot y) \ cdot z = x \cdot (y \cdot z )$. Will be say that for $ a, b \in S $, \ \ $ a \mathcal{R}^* b $ if and only if, for all $ x, and \in S^1 $ \ \ $ ax = ay $ if and only if $ bx = by $. Also, will be say that $ a \mathcal{L}^*b $ if and only if for all $ x, y \in S^1$ we have that $ xa = ya $ if and only if $xb = yb$. A element $ e $ front to semigroup $ S $ it's called idempotent when $ e^2 = e$. Will be say that semigroups it's left ample when each $\mathcal{R}^*-class $ it has at most to idempotent and all idempotent commute. Also must comply that $ ae = (ae)^\dagger a $, with $a,e^2=e\in S$. will be denote $E(S)$ the set of all idempotents from $S$ and additionally we will give its elements a order $\leq$ called natural order when $e\leq f$ if and only if $ef=fe=e$ will be defined an a idempotent as a primitive if for all $e\leq f$ it implies $f=e$ or $f=0$. Will be that a semigroups is primitive if all its idempotents are primitive. In the final part of the work will be Build a primitive ample Rees matrix and will be create a isomorphism with the primitive ample semigroups in which $aS\neq\{0\}.$ for $a\in S$ called as in \cite{AG06a} PLARI-semigroups.