Rengasteoria

Rengasteoria on algebran osa-alue, jonka tutkimuskohteena ovat renkaat – algebralliset rakenteet, joille on määritelty yhteen- ja kertolasku.

 Vaihdannaiset renkaat 

Rengasta kutsutaan vaihdannaiseksi, jos sen kertolasku on vaihdannainen. Jos  on rengas, jossa on määritelty yhteenlasku () ja kertolasku (), niin  on vaihdannainen, jos mille tahansa alkioille  pätee . Esimerkkejä vaihdannaisista renkaista ovat polynomirenkaat, algebrallisten kokonaislukujen renkaat samoin kuin tavalliset kokonaisluvut, ja p-aditiset kokonaisluvut.Michael Atiyah & Ian G. Macdonald, Introduction to Commutative Algebra, Massachusetts : Addison-Wesley Publishing, 1969. Kappale 1

 Kirjallisuutta 
 Suomeksi 


 Englanniksi 

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Pierce, Richard S. (1982), Associative Algebras, Graduate Texts in Mathematics, 88, New York: Springer-Verlag, , MR 0674652

Rowen, Louis H. (1988), Ring Theory, Vol. I, Pure and Applied Mathematics, 127, Boston, MA: Academic Press, , MR 0940245. Vol. II, Pure and Applied Mathematics 128, .

Weibel, Charles A. (2013), The K-book: An introduction to algebraic K-theory, Graduate Studies in Mathematics, 145, Providence, RI: American Mathematical Society, , MR 3076731

 Lähteet 

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