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 R on rengas, jossa on määritelty yhteenlasku (+) ja kertolasku (\cdot), niin R on vaihdannainen, jos mille tahansa alkioille a, b \in R pätee a\cdot b=b\cdot a. 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 === *Allenby, R. B. J. T. (1991), Rings, Fields and Groups (Second ed.), Edward Arnold, London, p. xxvi+383, ISBN 0-7131-3476-3, MR 1144518 *Blyth, T.S.; Robertson, E.F. (1985), Groups, Rings and Fields: Algebra through practice, Book 3, Cambridge: Cambridge University Press, ISBN 0-521-27288-2 *Faith, Carl (1999), Rings and Things and a Fine Array of Twentieth Century Associative Algebra, Mathematical Surveys and Monographs, 65, Providence, RI: American Mathematical Society, ISBN 0-8218-0993-8, MR 1657671 *Goodearl, K. R.; Warfield, R. B., Jr. (1989), An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts, 16, Cambridge: Cambridge University Press, ISBN 0-521-36086-2, MR 1020298 *Judson, Thomas W. (1997), Abstract Algebra: Theory and Applications *Kimberling, Clark (1981), "Emmy Noether and Her Influence", in Brewer, James W; Smith, Martha K, Emmy Noether: A Tribute to Her Life and Work, Marcel Dekker, pp. 3–61 *Lam, T. Y. (1999), Lectures on Modules and Rings, Graduate Texts in Mathematics, 189, New York: Springer-Verlag, doi:10.1007/978-1-4612-0525-8, ISBN 0-387-98428-3, MR 1653294 *Lam, T. Y. (2001), A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131 (Second ed.), New York: Springer-Verlag, doi:10.1007/978-1-4419-8616-0, ISBN 0-387-95183-0, MR 1838439 *Lam, T. Y. (2003), Exercises in Classical Ring Theory, Problem Books in Mathematics (Second ed.), New York: Springer-Verlag, ISBN 0-387-00500-5, MR 2003255 *Matsumura, Hideyuki (1980), Commutative Algebra, Mathematics Lecture Note Series, 56 (Second ed.), Reading, Mass.: Benjamin Cummings, ISBN 0-8053-7026-9, MR 0575344 *McConnell, J. C.; Robson, J. C. (2001), Noncommutative Noetherian Rings, Graduate Studies in Mathematics, 30, Providence, RI: American Mathematical Society, doi:10.1090/gsm/030, ISBN 0-8218-2169-5, MR 1811901 *O'Connor, J. J.; Robertson, E. F. (September 2004), "The development of ring theory", MacTutor History of Mathematics Archive *Pierce, Richard S. (1982), Associative Algebras, Graduate Texts in Mathematics, 88, New York: Springer-Verlag, ISBN 0-387-90693-2, MR 0674652 *Rowen, Louis H. (1988), Ring Theory, Vol. I, Pure and Applied Mathematics, 127, Boston, MA: Academic Press, ISBN 0-12-599841-4, MR 0940245. Vol. II, Pure and Applied Mathematics 128, ISBN 0-12-599842-2. *Weibel, Charles A. (2013), The K-book: An introduction to algebraic K-theory, Graduate Studies in Mathematics, 145, Providence, RI: American Mathematical Society, ISBN 978-0-8218-9132-2, MR 3076731 == Lähteet == *