Liu’s Reviews > A Course in Algebra > Status Update
Liu
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1. Nonzero elements of a field K form an abelian group with respect to multiplication. It is called the multiplicative group of K and is denoted K*.
2. If A is an associative ring with unity, the set of its invertible elements is a multiplicative group as well. We denote this group as A*.
— May 21, 2014 02:30AM
2. If A is an associative ring with unity, the set of its invertible elements is a multiplicative group as well. We denote this group as A*.
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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\.
