You forgot to add the remainder and most important piece of your definition of monopoly. THERE MUST BE A BARRIER.

Simple: A situation in which a single company owns all or nearly all of the market for a given type of product or service. This would happen in the case that there is a barrier to entry into the industry that allows the single company to operate without competition i.e. government regulation.

Walmart is not a monopoly, Microsoft is not a monoply, Anheuser Busch is not a monopoly and the AMA is not a monopoly, they are market leaders, a big difference. A monopoly is when you have actual control over these markets to knock out your competition with methods other then just your market presence.