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
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...
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...
Ethan Campbell, The Gawain-Poet and Fourteenth-Century English Anti-Clerical Tradition. Research in Medieval and Early Modern Culture. Kalamazoo, MI: Medieval Institute Publications / Western Michigan University, 2018, pp. 238.
Ethan Campbell, The Gawain-Poet and Fourteenth-Century English Anti-Clerical Tradition. Research in Medieval and Early Modern Culture. Kalamazoo, MI: Medieval Institute Publications / Western Michigan University, 2018, pp. 238.
In the past four years, there has been a flurry of valuable new work on the poems of the Gawain-poet (also known as the Pearl-poet), which includes new editions, translations, mono...
Phytochemical and Pharmacological Analysis of Moringa Oleifera Leaves
Phytochemical and Pharmacological Analysis of Moringa Oleifera Leaves
The use of medicinal plant extract-mediated treatment was found to be very effective in controlling bacterial infection. The plant moringa oleifera leaves was evaluated against gra...
Evaluation and validation of tungsten fiducial marker-based image-guided radiotherapy
Evaluation and validation of tungsten fiducial marker-based image-guided radiotherapy
Abstract
In this research work, a simple homemade cubic phantom was designed to validate the Image-Guided Radiotherapy (IGRT) set up and verified with the help of...