Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of genera...Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.展开更多
A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper...A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.展开更多
Let R be a ring. Recall that a right R-module M (RR, resp.) is said to be a PS-module (PS-ring, resp.) if it has projective socle. M is called a CESS-module if every complement summand in M with essential socle is a d...Let R be a ring. Recall that a right R-module M (RR, resp.) is said to be a PS-module (PS-ring, resp.) if it has projective socle. M is called a CESS-module if every complement summand in M with essential socle is a direct summand of M. We show that the formal triangular matrix ring T = A 0M B is a PS-ring if and only if A is a PS-ring, MA and lB(M) = {b ∈ B | bm = 0,m ∈ M} are PS-modules and Soc(lB(M)) M = 0. Using the alternative of right T-module as triple (X,Y )f with X ∈ Mod-A, Y ∈ Mod-B and f : YM →...展开更多
We study these rings with every minimal left ideal being a projective, direct summand and a p-injective module, respectively. Some characterizations of these rings are given, and the relations among them are obtained....We study these rings with every minimal left ideal being a projective, direct summand and a p-injective module, respectively. Some characterizations of these rings are given, and the relations among them are obtained. With these rings, we characterize seinisiinple rings. Finally, we introduce MC2 rings, and give some characterizations of MC2 rings.展开更多
A simple and novel method is firstly reported for controlling coffee ring structure on polystyrene（PS）film surface by O2 plasma. O2 plasma treatment leads to the wettability change of PS surface from hydrophobic to ...A simple and novel method is firstly reported for controlling coffee ring structure on polystyrene（PS）film surface by O2 plasma. O2 plasma treatment leads to the wettability change of PS surface from hydrophobic to hydrophilic. For hydrophilic PS surface the coffee ring structure is avoided relying on the motion of contact line（CL） while SiO2 microspheres are left. The motion of the CL is produced based on the viscosity and Marangoni effect with the addition of polymer additives. For hydrophobic PS surface coffee ring structure still persists even with polymer additives because SiO2 microspheres transfer with the motion of the CL at the beginning of droplet evaporation and accumulate at the droplet edge at late stage with the pinning of the CL. As a result, uniform and macroscale SiO2 microspheres deposition without coffee ring structure and SiO2 microspheres deposition with coffee ring structure are controlled by O2 plasma. This method provides a new way to tune coffee ring structure with smart surface and may be potentially useful for a range of application at material deposition and diagnosing diseases.展开更多
基金The NNSF (10171082) of China and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.
文摘Let R be a commutative ring and (S, ≤) a strictly totally ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. In this paper we show that if RM is a PS-module, then the module [[MS≤]] of generalized power series over M is a PS [[RS,≤]]-module.
文摘A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.
基金the National Natural Science Foundation of China (No.10171082)TRAPOYT (No.200280)Yong Teachers Research Foundation of NWNU (No.NWNU-QN-07-36)
文摘Let R be a ring. Recall that a right R-module M (RR, resp.) is said to be a PS-module (PS-ring, resp.) if it has projective socle. M is called a CESS-module if every complement summand in M with essential socle is a direct summand of M. We show that the formal triangular matrix ring T = A 0M B is a PS-ring if and only if A is a PS-ring, MA and lB(M) = {b ∈ B | bm = 0,m ∈ M} are PS-modules and Soc(lB(M)) M = 0. Using the alternative of right T-module as triple (X,Y )f with X ∈ Mod-A, Y ∈ Mod-B and f : YM →...
基金Project supported by the Foundation of Natural Science of China (19971073)the Natural Science Foundation of Jiangsu Province
文摘We study these rings with every minimal left ideal being a projective, direct summand and a p-injective module, respectively. Some characterizations of these rings are given, and the relations among them are obtained. With these rings, we characterize seinisiinple rings. Finally, we introduce MC2 rings, and give some characterizations of MC2 rings.
基金supported by the National Nature Science Foundation (Nos. 91123031, 20921003, 51403076, 21103112)he National Basic Research Program of China (No. 2012CB933802)
文摘A simple and novel method is firstly reported for controlling coffee ring structure on polystyrene（PS）film surface by O2 plasma. O2 plasma treatment leads to the wettability change of PS surface from hydrophobic to hydrophilic. For hydrophilic PS surface the coffee ring structure is avoided relying on the motion of contact line（CL） while SiO2 microspheres are left. The motion of the CL is produced based on the viscosity and Marangoni effect with the addition of polymer additives. For hydrophobic PS surface coffee ring structure still persists even with polymer additives because SiO2 microspheres transfer with the motion of the CL at the beginning of droplet evaporation and accumulate at the droplet edge at late stage with the pinning of the CL. As a result, uniform and macroscale SiO2 microspheres deposition without coffee ring structure and SiO2 microspheres deposition with coffee ring structure are controlled by O2 plasma. This method provides a new way to tune coffee ring structure with smart surface and may be potentially useful for a range of application at material deposition and diagnosing diseases.
