Hello :)

Burris and Sankappanavar define an "equational class" to be a class A
of algebras such that A is precisely the class of algebras of some type
F satisfying a set Sigma of identities of type F.

My question is, is there a special name for an equational class which
is precisely the class of algebras of some type F satisfying a _finite_
set Sigma of identities of type F? Or in English, the algebras that
can be axiomatized by finitely many identities?

Thank you very much =)

In article <1161370602.184339.216560@e3g2000cwe.googlegroups.com>,
Snis Pilbor <snispilbor@yahoo.com> wrote:
Hello :)

Burris and Sankappanavar define an "equational class" to be a class A
of algebras such that A is precisely the class of algebras of some type
F satisfying a set Sigma of identities of type F.

My question is, is there a special name for an equational class which
is precisely the class of algebras of some type F satisfying a _finite_
set Sigma of identities of type F? Or in English, the algebras that
can be axiomatized by finitely many identities?

Thank you very much =)

Such equational classes are said to be "finitely based".

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

Arturo Magidin wrote:
In article <1161370602.184339.216560@e3g2000cwe.googlegroups.com>,
Snis Pilbor <snispilbor@yahoo.com> wrote:
Hello :)

Burris and Sankappanavar define an "equational class" to be a class A
of algebras such that A is precisely the class of algebras of some type
F satisfying a set Sigma of identities of type F.

My question is, is there a special name for an equational class which
is precisely the class of algebras of some type F satisfying a _finite_
set Sigma of identities of type F? Or in English, the algebras that
can be axiomatized by finitely many identities?

Thank you very much =)

Such equational classes are said to be "finitely based".


Thank you very much Arturo Magidin =) As always, you are the
unchallenged master of UA

One more question. If we have a variety, by Birkhoff, it is an
equational class. If it happily turns out to be a finitely based
equational class, is it proper to refer to it as a "finitely based
variety"??