Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subr...Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.展开更多
We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achi...We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achieve singlefrequency operation.The experimentally measured optical signal-to-noise ratio is greater than 73 dB.Furthermore,the linewidth of the EDFL is measured to be about 480 Hz by the self-built short-delayed self-heterodyne interferometry device.The laser shows superior stability,with no mode-hopping during the 60-min observation period.The proposed EDFL provides a new experimental idea for realizing a single-frequency fiber laser in the L-band.展开更多
We propose and experimentally demonstrate compact on-chip 1×2 wavelength selective switches(WSSs) based on silicon microring resonators(MRRs) with nested pairs of subrings(NPSs). Owing to the resonance splitting ...We propose and experimentally demonstrate compact on-chip 1×2 wavelength selective switches(WSSs) based on silicon microring resonators(MRRs) with nested pairs of subrings(NPSs). Owing to the resonance splitting induced by the inner NPSs, the proposed devices are capable of performing selective channel routing at certain resonance wavelengths of the outer MRRs. System demonstration of dynamic channel routing using fabricated devices with one and two NPSs is carried out for 10 Gb∕s non-return-to-zero signal. The experimental results verify the effectiveness of the fabricated devices as compact on-chip WSSs.展开更多
In this paper,the Jacobson radical of (R[G])^G, the fixed point subring of a group ring (R[G]) is studied. Some related properties of (R[G])^G are discussed.
First, some properties of H separable rings are discussed, and it is shown that the H separable ring A can be represented as the tensor product of its subrings under certain conditions. Secondly, a neces...First, some properties of H separable rings are discussed, and it is shown that the H separable ring A can be represented as the tensor product of its subrings under certain conditions. Secondly, a necessary and sufficient condition is obtained for a Hopf Galois extension A/B to be H separable. Finally, some equivalent conditions are got for an H separable ring A to be a Hopf Galois extension over a certain subring B .展开更多
文摘Let R be an infinite ring with a maximal finite subring. We prove that R has a largest finite ideal and a largest finite nilpotent ideal N By a B ring, we mean an infinite ring with 1 containing a maximal finite subring which is a subfield containing 1. It is shown that R/NUVW, where U is a finite ring, V is a finite direct sum of matrix rings over B rings, and W is a ring containing no nonzero finite subrings.
基金supported by the Shaanxi Key Science and Technology Innovation Team Project(No.2023-CX-TD-06)。
文摘We demonstrate a stable narrow linewidth single-frequency erbium-doped fiber laser(EDFL)operating at 1.6μm.A Fabry–Perot fiber Bragg grating and two cascaded subrings are incorporated in the main ring cavity to achieve singlefrequency operation.The experimentally measured optical signal-to-noise ratio is greater than 73 dB.Furthermore,the linewidth of the EDFL is measured to be about 480 Hz by the self-built short-delayed self-heterodyne interferometry device.The laser shows superior stability,with no mode-hopping during the 60-min observation period.The proposed EDFL provides a new experimental idea for realizing a single-frequency fiber laser in the L-band.
基金supported in part by the National Natural Science Foundation of China under Grant 61125504/61235007in part by the 863 High-Tech Program under Grant 2013AA013402
文摘We propose and experimentally demonstrate compact on-chip 1×2 wavelength selective switches(WSSs) based on silicon microring resonators(MRRs) with nested pairs of subrings(NPSs). Owing to the resonance splitting induced by the inner NPSs, the proposed devices are capable of performing selective channel routing at certain resonance wavelengths of the outer MRRs. System demonstration of dynamic channel routing using fabricated devices with one and two NPSs is carried out for 10 Gb∕s non-return-to-zero signal. The experimental results verify the effectiveness of the fabricated devices as compact on-chip WSSs.
基金Supported by the NSF of Educational Department of Henan Province(20025100003)
文摘In this paper,the Jacobson radical of (R[G])^G, the fixed point subring of a group ring (R[G]) is studied. Some related properties of (R[G])^G are discussed.
文摘First, some properties of H separable rings are discussed, and it is shown that the H separable ring A can be represented as the tensor product of its subrings under certain conditions. Secondly, a necessary and sufficient condition is obtained for a Hopf Galois extension A/B to be H separable. Finally, some equivalent conditions are got for an H separable ring A to be a Hopf Galois extension over a certain subring B .
