#### 7.2.7.2 ring operations (plural)

`+`
  construct a tensor product of two -algebras and over the ground field. Let, e.g.,

  , and

  be two -algebras, then is defined to be the algebra

  , , .

Concerning the ground fields resp. of resp. , take the following guidelines for into consideration:

- Neither nor may be or .
- If the characteristic of and differs, then one of them must be .
- At most one of and may have parameters.
- If one of and is an algebraic extension of it may not be defined by a `charstr` of type `(p^n,a)`.

One can create a ring using `ring(list)`, see also `ringlist`.

Example:

    LIB "ncalg.lib";
    def a = makeUsl2();       // U(sl_2) in e,f,h presentation
    ring W0 = 0,(x,d),dp;
    def W = Weyl();              // 1st Weyl algebra in x,d
    def S = a+W;
    setring S;
    S;
    ==> // coefficients: QQ considered as a field
    ==> // number of vars : 5
    ==> //        block   1 : ordering dp
    ==> //                  : names    e f h
    ==> //        block   2 : ordering dp
    ==> //                  : names    x d
    ==> //        block   3 : ordering C
    ==> // noncommutative relations:
    ==> //    fe=ef-h
    ==> //    he=eh+2e
    ==> //    hf=fh-2f
    ==> //    dx=xd+1

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