algebra over a ring vs multiplication

algebra over a ring

noun
  • A module (over some ring) with an additional binary operation, a module-element-valued product between module elements, which is bilinear over module addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the module multiplication with respect to the module addition, which means that such a module is also a ring.) 

multiplication

noun
  • The process of computing the sum of a number with itself a specified number of times, or any other analogous binary operation that combines other mathematical objects. 

  • The process of multiplying or increasing in number; increase. 

  • A calculation involving multiplication. 

How often have the words algebra over a ring and multiplication occurred in a corpus of books? (source: Google Ngram Viewer )