Sentence:  If \le is an ordering on A compatible with its ring structure, we shall say that (A,\ +,\ \cdot,\le) is an <WSD>ordered ring</WSD>. An element x of an <WSD>ordered ring</WSD> A is positive if x\ge 0, and x is strictly positive if x>0. / The set of all positive elements of an <WSD>ordered ring</WSD> A is denoted by A_+, and the set of all strictly positive elements of A is denoted by A^_+. / If (A,\ +,\ \cdot,\le) is an <WSD>ordered ring</WSD> and if \le is a total ordering, we shall, of course, call (A,\ +,\ \cdot,\le) a <WSD>totally ordered ring</WSD>; if (A,\ +,\ \cdot) is a field, we shall call (A,\ +,\ \cdot,\le) an <WSD>ordered field</WSD>, and if, moreover, \le is a total ordering, we shal call (A,\ +\ \cdot,\le) a totally ordered field. 
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".