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
In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also a...In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.展开更多
We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class ...We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability.展开更多
Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R...Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R）. Phrthermore, we prove that, for any A ∈ Mn（R）（n ≥ 2）, there exists a U ∈ GLn（R） such that A ± U ∈ GLn（R）.展开更多
A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left (right) semicentral if for every x ∈ I,xe=exe (ex=exe).And I is called semiabelian if every idempot...A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left (right) semicentral if for every x ∈ I,xe=exe (ex=exe).And I is called semiabelian if every idempotent in I is left or right semicentral.It is proved that a semiabelian general ring I is π-regular if and only if the set N (I) of nilpotent elements in I is an ideal of I and I /N (I) is regular.It follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-regular.Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring.These generalize several known results on the relevant subject.Furthermore we give a characterization of a semiabelian GVNL-ring.展开更多
A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is th...A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J（R）^2.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.
An ATM ring switching testbed is proposed in this paper. Two practical applications for the ATMring exchange are aimed, one is used ai ATM LAM/MAN, another is for rural local ATM exchange. A dis-tributed swithching an...An ATM ring switching testbed is proposed in this paper. Two practical applications for the ATMring exchange are aimed, one is used ai ATM LAM/MAN, another is for rural local ATM exchange. A dis-tributed swithching and control architecture is designed. together with a modular and flexible hardware and soft-ware structure which permits a rapid and easy introduction and testing of new, services. Hierarchical VP and VCswitching is organized, three AALs (AAL1, AAL4 & AAL5) are supported to provide conaretion-oriented andconnectionless services Broadcasting, multicasting and multi-conferencing functions are achieved at no extra cost,and imerworking with the existing network is emphasized. The constucticon of ring access node is described. As anexample a PDH-ATM interface is given.展开更多
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.
基金This work is supported by the National Natural Science Foundation of China (Grant No.19801012)the Ministry of Education of China.
文摘In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.
基金This work is supported by the National Natural Science Foundation of China (Grant No. 19801012. 19531020).
文摘We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability.
基金Supported by Natural Science Foundation of Hunan Province(04JJ40003)
文摘Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R）. Phrthermore, we prove that, for any A ∈ Mn（R）（n ≥ 2）, there exists a U ∈ GLn（R） such that A ± U ∈ GLn（R）.
基金The NSF (Y2008A04) of Shandong Province of China
文摘A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left (right) semicentral if for every x ∈ I,xe=exe (ex=exe).And I is called semiabelian if every idempotent in I is left or right semicentral.It is proved that a semiabelian general ring I is π-regular if and only if the set N (I) of nilpotent elements in I is an ideal of I and I /N (I) is regular.It follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-regular.Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring.These generalize several known results on the relevant subject.Furthermore we give a characterization of a semiabelian GVNL-ring.
文摘A ring R is a QB-ring provided that aR ＋ bR = R with a, b E R implies that there exists a y E R such that a＋ by ∈ Rq^-1. It is said that a ring R is a JB-ring provided that R/J（R） is a QB-ring, where J（R） is the Jacobson radical of R. In this paper, various necessary and sufficient conditions, under which a ring is a JB-ring, are established. It is proved that JB-rings can be characterized by pseudo-similarity. Furthermore, the author proves that R is a JB-ring iff so is R/J（R）^2.
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An ATM ring switching testbed is proposed in this paper. Two practical applications for the ATMring exchange are aimed, one is used ai ATM LAM/MAN, another is for rural local ATM exchange. A dis-tributed swithching and control architecture is designed. together with a modular and flexible hardware and soft-ware structure which permits a rapid and easy introduction and testing of new, services. Hierarchical VP and VCswitching is organized, three AALs (AAL1, AAL4 & AAL5) are supported to provide conaretion-oriented andconnectionless services Broadcasting, multicasting and multi-conferencing functions are achieved at no extra cost,and imerworking with the existing network is emphasized. The constucticon of ring access node is described. As anexample a PDH-ATM interface is given.
