Coverage for local/lib/python2.7/site-packages/sage/categories/ring_ideals.py : 38%

r""" 

Ring ideals 

""" 

from __future__ import absolute_import 

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

# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> 

# William Stein <wstein@math.ucsd.edu> 

# 2008-2009 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 .category_types import Category_ideal 

from .modules import Modules 

from sage.categories.rings import Rings 

_Rings = Rings() 

class RingIdeals(Category_ideal): 

""" 

The category of two-sided ideals in a fixed ring. 

EXAMPLES:: 

sage: Ideals(Integers(200)) 

Category of ring ideals in Ring of integers modulo 200 

sage: C = Ideals(IntegerRing()); C 

Category of ring ideals in Integer Ring 

sage: I = C([8,12,18]) 

sage: I 

Principal ideal (2) of Integer Ring 

See also: :class:`CommutativeRingIdeals`. 

.. TODO:: 

- If useful, implement ``RingLeftIdeals`` and ``RingRightIdeals`` 

of which ``RingIdeals`` would be a subcategory. 

- Make ``RingIdeals(R)``, return ``CommutativeRingIdeals(R)`` 

when ``R`` is commutative. 

""" 

def __init__(self, R): 

""" 

EXAMPLES:: 

sage: RingIdeals(ZZ) 

Category of ring ideals in Integer Ring 

sage: RingIdeals(3) 

Traceback (most recent call last): 

... 

TypeError: R (=3) must be a ring 

TESTS:: 

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

""" 

if not R in _Rings: 

raise TypeError("R (=%s) must be a ring"%R) 

Category_ideal.__init__(self, R) 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: RingIdeals(ZZ).super_categories() 

[Category of modules over Integer Ring] 

sage: RingIdeals(QQ).super_categories() 

[Category of vector spaces over Rational Field] 

""" 

R = self.ring() 

return [Modules(R)]