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r""" 

Left modules 

""" 

from __future__ import absolute_import 

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

# Copyright (C) 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> 

# 

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

# http://www.gnu.org/licenses/ 

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

 

from .category_types import Category_over_base_ring 

from sage.categories.commutative_additive_groups import CommutativeAdditiveGroups 

 

#?class LeftModules(Category_over_base_rng): 

class LeftModules(Category_over_base_ring): 

""" 

The category of left modules 

left modules over an rng (ring not necessarily with unit), i.e. 

an abelian group with left multiplication by elements of the rng 

 

EXAMPLES:: 

 

sage: LeftModules(ZZ) 

Category of left modules over Integer Ring 

sage: LeftModules(ZZ).super_categories() 

[Category of commutative additive groups] 

 

TESTS:: 

 

sage: TestSuite(LeftModules(ZZ)).run() 

""" 

 

def super_categories(self): 

""" 

EXAMPLES:: 

 

sage: LeftModules(QQ).super_categories() 

[Category of commutative additive groups] 

""" 

return [CommutativeAdditiveGroups()] 

 

class ParentMethods: 

pass 

 

class ElementMethods: 

## r * x 

pass