Sentence:  D<small>EFINITION</small> 1. — "Given a commutative ring A, we say that an ordering on A is compatible with the ring structure on A if it is compatible with the additive group structure of A, and if it satisfies the following axiom:" / (OR) "The relations x \ge 0 and y \ge 0 imply xy \ge 0." / The ring A, together with such an ordering, is called an <WSD>"ordered ring</WSD>". / "Examples." — 1) The rings \Q and \Z, with the usual orderings, are <WSD>ordered rings</WSD>. / 2) A product of <WSD>ordered rings</WSD>, equipped with the product ordering, is an <WSD>ordered ring</WSD>. In particular, the ring A^E of mappings from a set E to an <WSD>ordered ring</WSD> A is an <WSD>ordered ring</WSD>. / 3) A subring of an <WSD>ordered ring</WSD>, with the induced ordering, is an <WSD>ordered ring</WSD>. 
Meaning of the word marked with <WSD> tags:  A ring, "R", equipped with a partial order, ≤, such that for arbitrary "a, b, c" ∈ "R", if "a" ≤ "b" then "a + c" ≤ "b + c", and if, additionally, 0 ≤ "c", then both "ca" ≤ "cb" and "ac" ≤ "bc".