Coverage for local/lib/python2.7/site-packages/sage/categories/associative_algebras.py : 0%

r""" 

Associative algebras 

""" 

#***************************************************************************** 

# Copyright (C) 2011 Nicolas M. Thiery <nthiery at users.sf.net> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.misc.lazy_import import LazyImport 

from sage.categories.category_with_axiom import CategoryWithAxiom_over_base_ring 

from sage.categories.magmas import Magmas 

from sage.categories.magmatic_algebras import MagmaticAlgebras 

class AssociativeAlgebras(CategoryWithAxiom_over_base_ring): 

r""" 

The category of associative algebras over a given base ring. 

An associative algebra over a ring `R` is a module over `R` which 

is also a not necessarily unital ring. 

.. WARNING:: 

Until :trac:`15043` is implemented, :class:`Algebras` is the 

category of associative unital algebras; thus, unlike the name 

suggests, :class:`AssociativeAlgebras` is not a subcategory of 

:class:`Algebras` but of 

:class:`~.magmatic_algebras.MagmaticAlgebras`. 

EXAMPLES:: 

sage: from sage.categories.associative_algebras import AssociativeAlgebras 

sage: C = AssociativeAlgebras(ZZ); C 

Category of associative algebras over Integer Ring 

TESTS:: 

sage: from sage.categories.magmatic_algebras import MagmaticAlgebras 

sage: C is MagmaticAlgebras(ZZ).Associative() 

True 

sage: TestSuite(C).run() 

""" 

_base_category_class_and_axiom = (MagmaticAlgebras, "Associative") 

Unital = LazyImport('sage.categories.algebras', 'Algebras', at_startup=True)