Modern Algebra, Group Theory (II): To determine whether the system described is a group.G = a0, a1, a2, a3,…, a6 where ai.aj = ai+j if i+j < 7 and ai.aj = ai+j-7 if i+j ≥ 7 .

Modern Algebra Group Theory (II) To determine whether the system described is a group. G = a0, a1, a2, a3,…, a6 where ai.aj = ai+j if i+j < 7 and ai.aj = ai+j-7 if i+j ≥ 7 .

Modern Algebra, Group Theory (III): To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

Modern Algebra Group Theory (III) To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

Modern Algebra, Group Theory (IV): To determine whether the system described is a group. G = set of all integers, a.b ≡ a - b

Modern Algebra Group Theory (IV) To determine whether the system described is a group. G = set of all integers, a.b ≡ a + b

Indecomposable representations of quiver A_n

classify the indecomposable representations of the quiver A_n with the orientation: o -> o -> o -> ... -> o Personal note: I thnik Gabriel's theorem may help here but not sure how.

Modern Algebra, Group Theory (V): Determine whether the system described is a group. G = set of all positive integers, a.b = ab , the usual product of integers.

Modern Algebra Group Theory (V) Determine whether the system described is a group. G = set of all positive integers, a.b = ab , the usual product of integers.