Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent r...Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.展开更多
N-methyl-D-aspartate receptors(NMDARs) are a family of ionotropic glutamate receptors mainly known to mediate excitatory synaptic transmission and plasticity. Interestingly, low-dose NMDAR antagonists lead to increase...N-methyl-D-aspartate receptors(NMDARs) are a family of ionotropic glutamate receptors mainly known to mediate excitatory synaptic transmission and plasticity. Interestingly, low-dose NMDAR antagonists lead to increased, instead of decreased, functional connectivity;and they could cause schizophrenia-and/or antidepressant-like behavior in both humans and rodents. In addition, human genetic evidences indicate that NMDAR loss of function mutations underlie certain forms of epilepsy, a disease featured with abnormal brain hyperactivity. Together, they all suggest that under certain conditions,NMDAR activation actually lead to inhibition, but not excitation,of the global neuronal network. Apparently, these phenomena are rather counterintuitive to the receptor's basic role in mediating excitatory synaptic transmission. How could it happen? Recently, this has become a crucial question in order to fully understand the complexity of NMDAR function, particularly in disease. Over the past decades, different theories have been proposed to address this question. These include theories of "NMDARs on inhibitory neurons are more sensitive to antagonism", or "basal NMDAR activity actually inhibits excitatory synapse", etc. Our review summarizes these efforts, and also provides an introduction of NMDARs,inhibitory neurons, and their relationships with the related diseases.Advances in the development of novel NMDAR pharmacological tools, particularly positive allosteric modulators, are also included to provide insights into potential intervention strategies.展开更多
文摘Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.
基金sponsored by Shanghai Science and Technology Committee(No.17DZ1205402)
文摘N-methyl-D-aspartate receptors(NMDARs) are a family of ionotropic glutamate receptors mainly known to mediate excitatory synaptic transmission and plasticity. Interestingly, low-dose NMDAR antagonists lead to increased, instead of decreased, functional connectivity;and they could cause schizophrenia-and/or antidepressant-like behavior in both humans and rodents. In addition, human genetic evidences indicate that NMDAR loss of function mutations underlie certain forms of epilepsy, a disease featured with abnormal brain hyperactivity. Together, they all suggest that under certain conditions,NMDAR activation actually lead to inhibition, but not excitation,of the global neuronal network. Apparently, these phenomena are rather counterintuitive to the receptor's basic role in mediating excitatory synaptic transmission. How could it happen? Recently, this has become a crucial question in order to fully understand the complexity of NMDAR function, particularly in disease. Over the past decades, different theories have been proposed to address this question. These include theories of "NMDARs on inhibitory neurons are more sensitive to antagonism", or "basal NMDAR activity actually inhibits excitatory synapse", etc. Our review summarizes these efforts, and also provides an introduction of NMDARs,inhibitory neurons, and their relationships with the related diseases.Advances in the development of novel NMDAR pharmacological tools, particularly positive allosteric modulators, are also included to provide insights into potential intervention strategies.
