Rings: definition and examples
General · Mathematics
Study notes
Q: Is (ℤ₆,+,×) a ring? Is 2×2 matrices a commutative ring? ℤ₆: + abelian group ✓, × associative ✓, distributive ✓: RING! (With 1: [1]!) M₂(ℝ): ring ✓, but AB ≠ BA: NONCOMMUTATIVE ring! Example: [0 1;0 0][0 0;1 0] = [1 0;0 0] vs [0 0;0 1]: differ! Zero divisors: nonzero product zero!