# Singular

#### 7.2.7.2 ring operations (plural)

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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; ==> // characteristic : 0 ==> // 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