A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu...A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.展开更多
In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely gene...In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.展开更多
The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only...The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.展开更多
This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ...It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.展开更多
in this paper,we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the comparability.In addition,it is shown that.if I is a minimal two-sided ideal of a regular ring R,then...in this paper,we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the comparability.In addition,it is shown that.if I is a minimal two-sided ideal of a regular ring R,then I satisfies the Comparability if and only if I is separative.Furthermore,we prove that.for ideals with stable range one.Roth's problem has an affirmative solution.These extend the corresponding results on unit-regularity and one-sided unit-regularity.展开更多
In this paper. we study the endomorphism rings of regular modules.We give sufficient conditions on a regular projective module P such that End_R(P) has stable range one.
In this study,aerodynamic behaviors of swept and leaned blades were investigated.Axial and tangential blade curvatures impacts on compressor's operating parameters were analyzed separately.A commercial CFD program...In this study,aerodynamic behaviors of swept and leaned blades were investigated.Axial and tangential blade curvatures impacts on compressor's operating parameters were analyzed separately.A commercial CFD program which solves the Reynolds-averaged Navier-Stokes equations was used to find out the mentioned impact and the complicated flow field of transonic compressor-rotors.The CFD method that was used for solving flow field's equation was validated by experimental data of NASA Rotor 67.The results showed that the compressor with curved rotors had higher efficiency,rotor pressure ratio and stable operating range compared to the compressor with un-curved rotors.Using curved rotors mostly had higher impact on the overall stable operating range compared to the other operating parameters.Operating range involves choking point and stall point that were changed separately by using of bended blade.For finding the detailed impact of sweep and lean angle on transonic blades,various forms of lean and sweep angles were exerted to basic rotor.It was found that sweep angles increased overall operating range up to 30%,efficiency up to 2%and pressure ratio up to 1%.Leaning the blades increased the safe operating range,the pressure ratio and efficiency by 14%,4%and 2%respectively.展开更多
基金Foundation items:The National Natural Science Foundation of China (No.10571026)the Specialized Research Fund for the Doctoral Program ofHigher Education (No.20060286006)
文摘A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.
文摘In this paper we study the formal triangular matrix ring T =and give some necessary and sufficient conditions for T to be (strongly) separative, m-fold stable and unit 1-stable. Moreover, a condition for finitely generated projec-tive T-modules to have n in the stable range is given under the assumption that A and B are exchange rings.
基金The National Natural Science Foundation of China(No10571026),the Natural Science Foundation of Jiangsu Province(NoBK2005207), the Teaching and Research Award Program for Out-standing Young Teachers in Higher Education Institutions of MOE,PRC
文摘The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.
文摘This article introduces a new class of ideals, namely, the sπr ideals. It is shown that every regular square matrix over sπr ideals of a ring admits a diagonal reduction.
基金Supported by the Natural Science Foundation of China (19901009)
文摘It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.
基金supported by the National Natural Science Foundation of China (GrantNo.19801012)the Ministry of Education of China
文摘in this paper,we investigate ideals of regular rings and give several characterizations for an ideal to satisfy the comparability.In addition,it is shown that.if I is a minimal two-sided ideal of a regular ring R,then I satisfies the Comparability if and only if I is separative.Furthermore,we prove that.for ideals with stable range one.Roth's problem has an affirmative solution.These extend the corresponding results on unit-regularity and one-sided unit-regularity.
基金The author is supported by the NNSF of China (No. 19601009)
文摘In this paper. we study the endomorphism rings of regular modules.We give sufficient conditions on a regular projective module P such that End_R(P) has stable range one.
文摘In this study,aerodynamic behaviors of swept and leaned blades were investigated.Axial and tangential blade curvatures impacts on compressor's operating parameters were analyzed separately.A commercial CFD program which solves the Reynolds-averaged Navier-Stokes equations was used to find out the mentioned impact and the complicated flow field of transonic compressor-rotors.The CFD method that was used for solving flow field's equation was validated by experimental data of NASA Rotor 67.The results showed that the compressor with curved rotors had higher efficiency,rotor pressure ratio and stable operating range compared to the compressor with un-curved rotors.Using curved rotors mostly had higher impact on the overall stable operating range compared to the other operating parameters.Operating range involves choking point and stall point that were changed separately by using of bended blade.For finding the detailed impact of sweep and lean angle on transonic blades,various forms of lean and sweep angles were exerted to basic rotor.It was found that sweep angles increased overall operating range up to 30%,efficiency up to 2%and pressure ratio up to 1%.Leaning the blades increased the safe operating range,the pressure ratio and efficiency by 14%,4%and 2%respectively.
