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:: Volume 7, Issue 1 (Vol.7, No. 1, Spring 2021) ::
mr 2021, 7(1): 127-132 Back to browse issues page
On lattice of Basic Z-Ideals
Ali Taherifar
Yasouj University , ataherifar@yu.ac.ir
Abstract:   (547 Views)
 For an f-ring  with bounded inversion property, we show that  , the set of all basic z-ideals of , partially ordered by inclusion is a bounded distributive lattice. Also, whenever  is a semiprimitive ring, , the set of all basic -ideals of , partially ordered by inclusion is a bounded distributive lattice. Next, for an f-ring  with bounded inversion property, we prove that  is a complemented lattice and  is a semiprimitive ring if and only if  is a complemented lattice and  is a reduced ring if and only if the base elements for closed sets in the space  are open and  is semiprimitive if and only if the base elements for closed sets in the space  are open and  is reduced. As a result, whenever  (i.e., the ring of continuous functions), we have  is a complemented lattice if and only if  is a complemented lattice if and only if  is a -space../files/site1/files/71/12.pdf
Keywords: F-ring, lattice, Zariski topology, Semiprimitive ring, Reduced ring.
Full-Text [PDF 413 kb]   (100 Downloads)    
Type of Study: Original Manuscript | Subject: alg
Received: 2019/06/8 | Accepted: 2019/10/15 | Published: 2021/05/31 | ePublished: 2021/05/31
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Taherifar A. On lattice of Basic Z-Ideals. mr. 2021; 7 (1) :127-132
URL: http://mmr.khu.ac.ir/article-1-2961-en.html


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Volume 7, Issue 1 (Vol.7, No. 1, Spring 2021) Back to browse issues page
پژوهش‌های ریاضی Mathematical Researches
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