Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Rd-phantom and RD-Ext-phantom morphisms
View through CrossRef
A morphism f of left R-modules is called an RD-phantom morphism if the
induced morphism Tor1(R=aR,f)=0 for any a ? R. Similarly, a morphism g
of left R-modules is said to be an RD-Ext-phantom morphism if the induced
morphism Ext1(R=Ra,g)=0 for any a ? R. It is proven that a morphism f is
an RD-phantom morphism if and only if the pullback of any short exact
sequence along f is an RD-exact sequence; a morphism g is an RD-Ext-phantom
morphism if and only if the pushout of any short exact sequence along g is
an RD-exact sequence. We also characterize Pr?fer domains, left
P-coherent rings, left PP rings, von Neumann regular rings in terms of
RD-phantom and RD-Ext-phantom morphisms. Finally, we prove that every module
has an epic RD-phantom cover with the kernel RD-injective and has a monic
RD-Ext-phantom preenvelope with the cokernel RD-projective.
Title: Rd-phantom and RD-Ext-phantom morphisms
Description:
A morphism f of left R-modules is called an RD-phantom morphism if the
induced morphism Tor1(R=aR,f)=0 for any a ? R.
Similarly, a morphism g
of left R-modules is said to be an RD-Ext-phantom morphism if the induced
morphism Ext1(R=Ra,g)=0 for any a ? R.
It is proven that a morphism f is
an RD-phantom morphism if and only if the pullback of any short exact
sequence along f is an RD-exact sequence; a morphism g is an RD-Ext-phantom
morphism if and only if the pushout of any short exact sequence along g is
an RD-exact sequence.
We also characterize Pr?fer domains, left
P-coherent rings, left PP rings, von Neumann regular rings in terms of
RD-phantom and RD-Ext-phantom morphisms.
Finally, we prove that every module
has an epic RD-phantom cover with the kernel RD-injective and has a monic
RD-Ext-phantom preenvelope with the cokernel RD-projective.
Related Results
Correlates of Risk for Disinhibited Behaviors in the Million Veteran Program Cohort
Correlates of Risk for Disinhibited Behaviors in the Million Veteran Program Cohort
Importance
Many psychiatric outcomes share a common etiologic pathway reflecting behavioral disinhibition, generally referred to as externalizing (EXT) disorder...
Flavonoid-mediated biofilm inhibition and toxicological evaluation of Atriplex laciniata against multidrug-resistant MRSA
Flavonoid-mediated biofilm inhibition and toxicological evaluation of Atriplex laciniata against multidrug-resistant MRSA
Multidrug-resistant (MDR) superbugs threaten the efficacy of antibiotics, so new drug formulations from synthetic or natural sources are needed to combat antimicrobial-resistant (A...
Body image and perception among adults with and without phantom limb pain
Body image and perception among adults with and without phantom limb pain
AbstractBackgroundFollowing lower‐limb amputation, phantom limb pain (i.e., pain perceived as coming from the amputated portion of the limb) is common. Phantom limb pain may be ass...
Manuscripts in the Making. Art & Science. Volume One, ed. Stella Panaytotova and Paola Ricciardi. London and Turnhout: Harvey Miller, 2017, pp. 254.
Manuscripts in the Making. Art & Science. Volume One, ed. Stella Panaytotova and Paola Ricciardi. London and Turnhout: Harvey Miller, 2017, pp. 254.
This, the first of a planned two-volume set of thirty-four papers from the Fitzwilliam Museum’s conference (December 2016) at the University of Cambridge on the occasion of its bic...
Pierre Bouet und François Neveux, Der Teppich von Bayeux: Ein mittelalterliches Meisterwerk. Übersetzt von Heike Rosbach und Hanne Henninger. Darmstadt: Theiss, 2018, 236 S., zahlreiche farbige Abb.
Pierre Bouet und François Neveux, Der Teppich von Bayeux: Ein mittelalterliches Meisterwerk. Übersetzt von Heike Rosbach und Hanne Henninger. Darmstadt: Theiss, 2018, 236 S., zahlreiche farbige Abb.
Kaum ein anderes Textilkunstwerk des Mittelalters hat bis heute solch eine Bekanntheit errungen wie der Teppich von Bayeux. Die Forschung hat sich schon seit sehr langem intensiv d...
Effects of chronic paroxetine treatment on dialysate serotonin in 5‐HT1B receptor knockout mice
Effects of chronic paroxetine treatment on dialysate serotonin in 5‐HT1B receptor knockout mice
AbstractThe role of serotonin (5‐HT)1B receptors in the mechanism of action of selective serotonin re‐uptake inhibitors (SSRI) was studied by using intracerebral in vivo microdialy...
Bioactive Phenolics and Flavonoids, Antioxidants, Anti-Inflammatory, Enzyme-Inhibitory and Cytotoxic Activities of Aerial part of Trachyspermum roxburghianum (DC.) Craib.
Bioactive Phenolics and Flavonoids, Antioxidants, Anti-Inflammatory, Enzyme-Inhibitory and Cytotoxic Activities of Aerial part of Trachyspermum roxburghianum (DC.) Craib.
Trachyspermum roxburghianum (DC.) Craib is an edible plant found in Northern and Northeastern Thailand. This plant is used in household remedies to relieve carminative and digestiv...
Phytochemical and Bioassay Screening for the Fruits of Azadirachta Indica
Phytochemical and Bioassay Screening for the Fruits of Azadirachta Indica
The MeOH and aqueous Ext of A. indica fruits were found active against P. aeruginosa. The results of methanolic extract and Aq Ext showed good antibacterial activity against S. aur...