Liu’s Reviews > A Course in Algebra > Status Update
Liu
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Remark 1.83. Observe that all constructions in the last three sections (1.7 Vector spaces, 1.8 Algebras, 1.9 Matrix Algebra) would remain unchanged if we replaced K with a commutative associative ring with unity, for instance, the ring of integers or a ring of residue classes. The only difference lies in terminology: in this more general situation the term module is used instead of vector space (see Section 9.3).
— May 14, 2014 07:18PM
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Liu
is on page 167 of 511
Exercise 4.99. The sign of a cyclic permutation is sign(i1,i2,...,ip) = (-1)^(p-1)
— May 24, 2014 08:03PM
Liu
is on page 158 of 511
In a Monoid, the left e is the right e, and a left inverse is also the right one. Refer to Lang.
— May 22, 2014 08:02PM
Liu
is on page 157 of 511
Theorem 4.67 (Lagrange's Theorem). Let G be a finite group and H its
subgroup. Then
\G\ = \G:H\\H\.
— May 22, 2014 12:22PM
subgroup. Then
\G\ = \G:H\\H\.
