In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finit...In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.展开更多
Salt stress is an increasingly severe problem worldwide,resulting in production losses,developmental changes,and ion transport anomalies(Munns&Gilliham,2015).The extent of salinization damage has escalated globall...Salt stress is an increasingly severe problem worldwide,resulting in production losses,developmental changes,and ion transport anomalies(Munns&Gilliham,2015).The extent of salinization damage has escalated globally as a result of unsustainable irrigation practices and climate change(van Zelm et al.,2020).Populus simonii is used as a model forest species in studies of abiotic stress tolerance,due to its extraordinary capacity to adapt to salt,drought,cold,and heat stress(Song et al.,2014).In fact,some P.simonii varieties persist in soils with up to 5%salt content;however,the genetic basis of salt tolerance in this species has yet to be explored.展开更多
文摘In this paper,the author studies the regularity of Munn rings and completely 0- simple semigroup rings.When either(i)R is a ring with identity and I and A are infinite,or(ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or A is finite,in Section 2,the regularity of the Munn ring M(R;I,A;P)is characterized;in Section 3,for a completely 0-simple semigroup S= M°(G;I,A;P),the regularity of RS is characterized.Meantime,the author shows that for a locally finite monoid S and a ring R with identity,RS is a strong IBN ring if and only if R is so;RS is fully Dedekind-finite if and only if R is so.
基金supported by STI2030—Major Projects(No.2023ZD040710508)the Project of Youth talent program of Forestry and Grassland Science and Technology Innovation(No.2020132606)the 111 Project(No.B20050)。
文摘Salt stress is an increasingly severe problem worldwide,resulting in production losses,developmental changes,and ion transport anomalies(Munns&Gilliham,2015).The extent of salinization damage has escalated globally as a result of unsustainable irrigation practices and climate change(van Zelm et al.,2020).Populus simonii is used as a model forest species in studies of abiotic stress tolerance,due to its extraordinary capacity to adapt to salt,drought,cold,and heat stress(Song et al.,2014).In fact,some P.simonii varieties persist in soils with up to 5%salt content;however,the genetic basis of salt tolerance in this species has yet to be explored.
