One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summa...One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.展开更多
Powdery mildew(PM),caused by the biotrophic fungus Podospharea leucotricha,poses a significant threat to apple production.Salicylic acid(SA)signaling plays a crucial role in enhancing resistance to biotrophic pathogen...Powdery mildew(PM),caused by the biotrophic fungus Podospharea leucotricha,poses a significant threat to apple production.Salicylic acid(SA)signaling plays a crucial role in enhancing resistance to biotrophic pathogens.While PR1,a defense protein induced by SA,is essential for plant immunity,its excessive accumulation can be detrimental.However,the mechanism of PR1-mediated immune balance remains unclear.This study identified a key transcription factor,WRKY1,which enhances the SA accumulation by modulating the SA biosynthesis gene EPS1,while simultaneously regulating the WRKY40-NPR3g module to prevent sustained PR1 expression caused by continuous SA accumulation.Specifically,the transcription factor WRKY40 upregulates NPR3g expression,and NPR3g interacts with NPR1 in an SA-dependent manner.Then,two TGA2c variants that interact with NPR1 to activate PR1 expression were identified:canonical TGA2c-1 and alternative splicing of TGA2c-2 with an exon deletion.SA does not influence the NPR1-TGA2c-1 interaction but is essential for the NPR1-TGA2c-2 interaction.Notably,NPR3g reduces PR1 levels by selectively disrupting the NPR1-TGA2c-2 complex through competition for the BTB-POZ domain of NPR1.In conclusion,this study identifies a novel mechanism by which WRKY1 modulates PR1-mediated immune balance to defend against PM.展开更多
The two-dimensional(2D)C3 N has emerged as a material with promising applications in high performance device owing to its intrinsic bandgap and tunable electronic properties.Although there are several reports about th...The two-dimensional(2D)C3 N has emerged as a material with promising applications in high performance device owing to its intrinsic bandgap and tunable electronic properties.Although there are several reports about the bandgap tuning of C3 N via stacking or forming nanoribbon,bandgap modulation of bilayer C3 N nanoribbons(C3NNRS)with various edge structures is still far from well understood.Here,based on extensive first-principles calculations,we demonstrated the effective bandgap engineering of C3 N by cutting it into hydrogen passivated C3 NNRS and stacking them into bilayer heterostructures.It was found that armchair(AC)C3 NNRS with three types of edge structures are all semiconductors,while only zigzag(ZZ)C3NNRS with edges composed of both C and N atoms(ZZCN/CN)are semiconductors.The bandgaps of all semiconducting C3 NNRS are larger than that of C3 N nanosheet.More interestingly,AC-C3 NNRS with CN/CN edges(AC-CN/CN)possess direct bandgap while ZZ-CN/CN have indirect bandgap.Compared with the monolayer C3 NNR,the bandgaps of bilayer C3NNRS can be greatly modulated via different stacking orders and edge structures,varying from 0.43 eV for ZZ-CN/CN with AB’-stacking to 0.04 eV for AC-CN/CN with AA-stacking.Particularly,transition from direct to indirect bandgap was observed in the bilayer AC-CN/CN heterostructure with AA^stacking,and the indirect-to-direct transition was found in the bilayer ZZ-CN/CN with ABstacking.This work provides insights into the effective bandgap engineering of C3 N and offers a new opportunity for its applications in nano-electronics and optoelectronic devices.展开更多
文摘One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.
基金This research was supported by the National Natural Science Foundation of China(NSFC)through grant numbers 31171935 and 31560551.
文摘Powdery mildew(PM),caused by the biotrophic fungus Podospharea leucotricha,poses a significant threat to apple production.Salicylic acid(SA)signaling plays a crucial role in enhancing resistance to biotrophic pathogens.While PR1,a defense protein induced by SA,is essential for plant immunity,its excessive accumulation can be detrimental.However,the mechanism of PR1-mediated immune balance remains unclear.This study identified a key transcription factor,WRKY1,which enhances the SA accumulation by modulating the SA biosynthesis gene EPS1,while simultaneously regulating the WRKY40-NPR3g module to prevent sustained PR1 expression caused by continuous SA accumulation.Specifically,the transcription factor WRKY40 upregulates NPR3g expression,and NPR3g interacts with NPR1 in an SA-dependent manner.Then,two TGA2c variants that interact with NPR1 to activate PR1 expression were identified:canonical TGA2c-1 and alternative splicing of TGA2c-2 with an exon deletion.SA does not influence the NPR1-TGA2c-1 interaction but is essential for the NPR1-TGA2c-2 interaction.Notably,NPR3g reduces PR1 levels by selectively disrupting the NPR1-TGA2c-2 complex through competition for the BTB-POZ domain of NPR1.In conclusion,this study identifies a novel mechanism by which WRKY1 modulates PR1-mediated immune balance to defend against PM.
基金This work was supported by the National Natural Science Foundation of China(Grant No.21673075).
文摘The two-dimensional(2D)C3 N has emerged as a material with promising applications in high performance device owing to its intrinsic bandgap and tunable electronic properties.Although there are several reports about the bandgap tuning of C3 N via stacking or forming nanoribbon,bandgap modulation of bilayer C3 N nanoribbons(C3NNRS)with various edge structures is still far from well understood.Here,based on extensive first-principles calculations,we demonstrated the effective bandgap engineering of C3 N by cutting it into hydrogen passivated C3 NNRS and stacking them into bilayer heterostructures.It was found that armchair(AC)C3 NNRS with three types of edge structures are all semiconductors,while only zigzag(ZZ)C3NNRS with edges composed of both C and N atoms(ZZCN/CN)are semiconductors.The bandgaps of all semiconducting C3 NNRS are larger than that of C3 N nanosheet.More interestingly,AC-C3 NNRS with CN/CN edges(AC-CN/CN)possess direct bandgap while ZZ-CN/CN have indirect bandgap.Compared with the monolayer C3 NNR,the bandgaps of bilayer C3NNRS can be greatly modulated via different stacking orders and edge structures,varying from 0.43 eV for ZZ-CN/CN with AB’-stacking to 0.04 eV for AC-CN/CN with AA-stacking.Particularly,transition from direct to indirect bandgap was observed in the bilayer AC-CN/CN heterostructure with AA^stacking,and the indirect-to-direct transition was found in the bilayer ZZ-CN/CN with ABstacking.This work provides insights into the effective bandgap engineering of C3 N and offers a new opportunity for its applications in nano-electronics and optoelectronic devices.
