Two serial fields, PK identity

Hi!

1.
apache=> create table tmp2 (a serial, b serial, name text);
apache=> \ds
Database = apache
+------------------+----------------------------------+----------+
| Owner | Relation | Type |
+------------------+----------------------------------+----------+
| apache | tmp2_b_seq | sequence |
+------------------+----------------------------------+----------+

Where is tmp2_a_seq?
Why there can't be two serial fields at all and parser doesn't say me
about?

2. SERIAL type as PRIMARY KEY
For example:
apache=> create table tmp4 (a serial);
NOTICE: CREATE TABLE will create implicit sequence 'tmp4_a_seq' for SERIAL column 'tmp4.a'
NOTICE: CREATE TABLE/UNIQUE will create implicit index 'tmp4_a_key' for table 'tmp4'
CREATE
apache=> create table tmp5 (a serial primary key);
NOTICE: CREATE TABLE will create implicit sequence 'tmp5_a_seq' for SERIAL column 'tmp5.a'
NOTICE: CREATE TABLE/PRIMARY KEY will create implicit index 'tmp5_pkey' for table 'tmp5'
CREATE

So, I thing, if I use SERIAL I can omit PRIMARY KEY constraint, but
receive PK via SERIAL type.
Then I must define trigger or rule on UPDATE to keep PK IDENTITY.
Is it so?

Regards, Alexey V. Meledin
InterForge Developers Group, Saint-Petersburg
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