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Solutions for Assignment I - Modern Abstract Algebra | MAT 4233, Assignments of Abstract Algebra

University of Texas - San AntonioAbstract Algebra
Prof. Dmitry Gokhman

Material Type: Assignment; Professor: Gokhman; Class: Modern Abstract Algebra; Subject: Mathematics; University: University of Texas - San Antonio; Term: Spring 2009;

Typology: Assignments

Pre 2010

Uploaded on 07/30/2009

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Download Solutions for Assignment I - Modern Abstract Algebra | MAT 4233 and more Assignments Abstract Algebra in PDF only on Docsity!

36. Prove that / = (2 + 2/) is not a prime ideal of Z[i]. How many elements are in Z[i]/7? What is the characteristic of Z[i]//? oad {arbi + a bem ‘tab OGL bet aieslet caw yore: — {gat tet = Yo [eT tl ed =2T oR, nu tak ® [eT 14, Let A and B be ideals of a ring. Prove thatAB CAN B. wr be AS (ach, beB) Gina A on el a ach | beh pene Sue Bu a es al WER aves) Yo New pile a ened Qunuk in AB D aybe wheajeA Vek . 421 Qy above Tb GANS Grnee Ang fan teal) Barby € ANG 16, If A and B are ideals of a commutative ring R with unity and A + B= R, show thatA M B = AB. ler XE ANG | Thy xe A an xeB Fine ReAr® y le h+8 , se lz arb dv Gre «eA be@ y= x-le= x(a +h’) 2 Yat xb = ax +xb Siew xe R, ax ERG Since KX EA xbe AB So xe AB C