Let us suppose whe find a phenomenon (in nature, social sciences, whatever) for which we believe (or some author has stated) it is possible a formalization or modeling in terms of ideal of a ring. Let us further suppose, the possibility of a two-sided ideal is excluded (what specific feature of the phenomenon might exclude that?). My question is: which kind of property of the phenomenon or object of study would be responsible for the decision between a right or a left ideal of the ring? Any suggestions?
Thanks in advance.