1. Leopold Kronecker (Fundamental Theorem of Finite Abelian Groups)		a. Z_6={0,1,2,...,5} under +mod6 is the direct product of Z_2={0,1} under +mod2 and Z_3={0,1,2} under +mod3.
2. Marjorie Lee Browne		b. Z_3 is a finite field
3. Johann Carl Friedrich Gauss (Fundamental Theorem of Algebra)		c. Z_6={0,1,2,...,5} under +mod6 has a subgroup of order 2 Z_2={0,3} under +mod6 and a subgroup of order 3 Z_3={0,2,4} under +mod6.
4. Peter Ludwig Mejdell Sylow (Sylow's First Theorem)		d. 2x2 matrices with determinant 1 satisfying A times A transpose equals the identity form a group under matrix multiplication.
5. Sir William Rowan Hamilton		e. The quaternions are a ring that are not abelian under multiplication since ij=k, but ji=-k
6. Evariste Galois		f. When we adjoin any root r of f(x)=x^6+6x^5+17x^4+32x^3+37x^2+26x+6 to the complex numbers C, we still get C. I.e. C(r)=C for all roots r.
7. Emmy Amalie Noether		g. Z_6 is a ring but not a field
8. Julius Wihelm Richard Dedekind		h. Z satisfies the ACC condition on ideals since every ascending chain of ideals terminates at some point.

1	-->	Choose Match abcdefgh
2	-->	Choose Match abcdefgh
3	-->	Choose Match abcdefgh
4	-->	Choose Match abcdefgh
5	-->	Choose Match abcdefgh
6	-->	Choose Match abcdefgh
7	-->	Choose Match abcdefgh
8	-->	Choose Match abcdefgh

	1.	Z_6 is not finite
	2.	Z_6 is not a ring
	3.	Z_6 is not abelian under multiplication
	4.	Z_6 has no identity for multiplication
	5.	Z_6 violates that all non-zero elements have multiplicative inverses in Z_6

	1.	They are not a ring
	2.	They are not abelian under multiplication
	3.	They do not have an identity for mult
	4.	They have zero divisors