Addition and multiplication modulus.

May 19th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

modulus, multiplicative inverse, fields, and Rings

Word Count: 907
Showing Page: 1/5
Example.(Addition and multiplication mod 5)Construct addition and multiplication tables for.Notice in the multiplication table thatThis means that,, and. In particular, to divide by 2 you multiply by 3: in, the elements 2 and 3 arereciprocals.Commutative rings with identity come up in discussingdeterminants, but the algebraic system of greatest importance in linear algebra is thefield.Definition.Let R be a ring with identity, and let. Themultiplicative inverseof x is an elementwhich satisifiesDefinition.AfieldF is a commutative ring with identity in whichand every nonzero element has a multiplicative inverse.By convention, you don't write "" for "" unless the ring happens to be,, or.If an element x has a multiplicative inverse,you can divide byxby multiplying by. Thus, in a field, you can divide by any nonzero element. (You'll learn in abstract algebra why it doesn't make sense to divide by 0.)Example.The rationals, the reals, and the complex numbersare fields. Many of the examples will use these number systems.The ring of integersis not a field. For example, 2 is a nonzero integer, but it does not have a multiplicative inverse {\it which is an integer}. (is not an integer --- it's a rational number.),, andare all infinite fields --- that is, they all have infinitely many elements. For applications, it's important to considerfinitefields as well

Review from student

Studypool Student
" awesome work thanks "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1826 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors