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## First steps going down on algebraic frames

#### Themba DUBE [1]

We extend the ring-theoretic concept of going down  to algebraic frames and coherent maps. We then use the notion introduced to characterize algebraic frames of dimension 0 and frames of dimension at most 1. An application to rings yields a characterization of von Neumann regular rings that appears to have hitherto been overlooked. Namely, a commutative ring $A$ with identity is von Neumann regular if and only if $Ann(I)+P=A$, for every prime ideal $P$ of $A$ and any finitely generated ideal $I$ of $A$ contained in $P$.
Algebraic frame, Sublocale, Prime element, Going-down, Commutative ring, Dimension
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-2702-2192Author: Themba DUBE (Primary Author)Institution: University of South AfricaCountry: South Africa Publication Date : December 8, 2019
 Bibtex @research article { hujms480650, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1792 - 1807}, doi = {10.15672/HJMS.2018.638}, title = {First steps going down on algebraic frames}, key = {cite}, author = {DUBE, Themba} } APA DUBE, T . (2019). First steps going down on algebraic frames. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1792-1807 . DOI: 10.15672/HJMS.2018.638 MLA DUBE, T . "First steps going down on algebraic frames". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1792-1807 Chicago DUBE, T . "First steps going down on algebraic frames". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1792-1807 RIS TY - JOUR T1 - First steps going down on algebraic frames AU - Themba DUBE Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.638 DO - 10.15672/HJMS.2018.638 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1792 EP - 1807 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.638 UR - https://doi.org/10.15672/HJMS.2018.638 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics First steps going down on algebraic frames %A Themba DUBE %T First steps going down on algebraic frames %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.638 %U 10.15672/HJMS.2018.638 ISNAD DUBE, Themba . "First steps going down on algebraic frames". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1792-1807 . https://doi.org/10.15672/HJMS.2018.638 AMA DUBE T . First steps going down on algebraic frames. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1792-1807. Vancouver DUBE T . First steps going down on algebraic frames. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1807-1792.