Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new ch...Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.展开更多
In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a genera...In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a generalized EP element,i.e.,+-DMP element.展开更多
We first prove that if a is both left(6,c)-invertible and left(c,b)-invertible,then a is both(6,c)-invertible and(c,6)-invertible in a*-monoid,which generalizes the recent result about the inverse along an element by ...We first prove that if a is both left(6,c)-invertible and left(c,b)-invertible,then a is both(6,c)-invertible and(c,6)-invertible in a*-monoid,which generalizes the recent result about the inverse along an element by L.Wang and D.Mosic[Linear Multilinear Algebra,Doi.org/10.1080/03081087.2019.1679073],under the conditions(a6)*=ab and(ac)*=ac.In addition,we consider that ba is(c,fe)-invertible,and at the same time ca is(6,c)-invertible under the same conditions,which extend the related results about Moore-Penrose inverses studied by J.Chen,H.Zou,H.Zhu,and P.Patricio[Mediterr J.Math.,2017,14:208]to(6,c)-inverses.As applications,we obtain that under condition(a2)^(*)=a^(2),a is an EP element if and only if a is one-sided core invertible,if and only if a is group invertible.展开更多
In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of 1−pq,1−pqp,p−pq and p−q,where p,q are projections in different settings,such as∗-rings,∗-reducing rings and C∗-algebras.More...In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of 1−pq,1−pqp,p−pq and p−q,where p,q are projections in different settings,such as∗-rings,∗-reducing rings and C∗-algebras.Moreover,several representations for the core inverses of product,difference and sum of two generalized projections are derived.In particular,a number of examples are given to illustrate our results.展开更多
The cause of virulence decline of hypovirulent isolate Ep-1PN of Sclerotinia sclerotiorum (Lib.) de Bary has been studied through transmitting test and analysing its offsprings derived from single ascospore. When the ...The cause of virulence decline of hypovirulent isolate Ep-1PN of Sclerotinia sclerotiorum (Lib.) de Bary has been studied through transmitting test and analysing its offsprings derived from single ascospore. When the colony of a normal strain Ep-1PNA 183 intermingled with the colony of Ep-1PN, its margin became abnormal, just like Ep-1PN. Cultures isolated from top-tip of the colony of Ep-1PNA 183 showed the hypovirulence and its associated properties of Ep-1PN. Moreover, a series of cultures which have characteristics between Ep-1PN and normal strain could be isolated from stipes of Ep-1PN. More than 200 offsprings derived from single ascospore of Ep-1PN were normal strains. According to those results, there exists a transmissible cytoplasmic hypovirulent element in hypovirulent isolate Ep-1PN of S. sclerotiorum.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11201063,11771076)the Ministry of Education and Science,Republic of Serbia(No.174007)
文摘Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.
基金The research was supported by the Ministry of Education,Science and Technological Development(grant no.174007)Republic of Serbia,and by NSF of China(11901510)+1 种基金NSF of Jiangsu Province of China(BK20170589)China Postdoctoral Science Foundation Funded Project(2017M611920).
文摘In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a generalized EP element,i.e.,+-DMP element.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771076,11871145)the Fundamental Research Funds for the Central Universitiesthe Postgraduate Research&:Practice Innovation Program of Jiangsu Province(No.KYCX19-0055).
文摘We first prove that if a is both left(6,c)-invertible and left(c,b)-invertible,then a is both(6,c)-invertible and(c,6)-invertible in a*-monoid,which generalizes the recent result about the inverse along an element by L.Wang and D.Mosic[Linear Multilinear Algebra,Doi.org/10.1080/03081087.2019.1679073],under the conditions(a6)*=ab and(ac)*=ac.In addition,we consider that ba is(c,fe)-invertible,and at the same time ca is(6,c)-invertible under the same conditions,which extend the related results about Moore-Penrose inverses studied by J.Chen,H.Zou,H.Zhu,and P.Patricio[Mediterr J.Math.,2017,14:208]to(6,c)-inverses.As applications,we obtain that under condition(a2)^(*)=a^(2),a is an EP element if and only if a is one-sided core invertible,if and only if a is group invertible.
基金supported by the National Natural Science Foundation of China(No.11771076,11961076)the Ministry of Science,Technology and Development,Republic of Serbia(No.174007)+1 种基金the China Postdoctoral Science Foundation(No.2020M671281)the Research Project of Hubei Provincial Departmentof Education(No.B2019128).
文摘In this paper we obtain some equivalent conditions for the core invertibility and EP-ness of 1−pq,1−pqp,p−pq and p−q,where p,q are projections in different settings,such as∗-rings,∗-reducing rings and C∗-algebras.Moreover,several representations for the core inverses of product,difference and sum of two generalized projections are derived.In particular,a number of examples are given to illustrate our results.
文摘The cause of virulence decline of hypovirulent isolate Ep-1PN of Sclerotinia sclerotiorum (Lib.) de Bary has been studied through transmitting test and analysing its offsprings derived from single ascospore. When the colony of a normal strain Ep-1PNA 183 intermingled with the colony of Ep-1PN, its margin became abnormal, just like Ep-1PN. Cultures isolated from top-tip of the colony of Ep-1PNA 183 showed the hypovirulence and its associated properties of Ep-1PN. Moreover, a series of cultures which have characteristics between Ep-1PN and normal strain could be isolated from stipes of Ep-1PN. More than 200 offsprings derived from single ascospore of Ep-1PN were normal strains. According to those results, there exists a transmissible cytoplasmic hypovirulent element in hypovirulent isolate Ep-1PN of S. sclerotiorum.
