Neat question...
Abelian Group: Z or Z/nZ
Nonabelian Group: Dihedral groups or GL_n
Commutative Ring: Z or C[x]
Noncommutative Ring: Matrix rings
Division Ring: Quaternions
Field: R or C
Lie Algebra: sl_2
Neat question...
Abelian Group: Z or Z/nZ
Nonabelian Group: Dihedral groups or GL_n
Commutative Ring: Z or C[x]
Noncommutative Ring: Matrix rings
Division Ring: Quaternions
Field: R or C
Lie Algebra: sl_2