This article describes the geographical indication characteristics of Zhuanbu strawberry,a special product of Yinan County,Shandong Province,a national geographical indication agricultural product,including specific p...This article describes the geographical indication characteristics of Zhuanbu strawberry,a special product of Yinan County,Shandong Province,a national geographical indication agricultural product,including specific production area,unique production environment,rich human history and unique product quality,summarizes the unique production method of Zhuanbu strawberry from selection of production area and varieties,production management,timely harvesting and other aspects,and puts forward corresponding industrial development measures,in order to maintain the brand of Zhuanbu strawberry to the greatest extent and further improve the brand awareness and market competitiveness of Zhuanbu strawberry.展开更多
Let R be an associative ring with identity and Z^*(K)be its set of non-zero zero-divisors.The undirected zero-divisor graph of R、denoted byΓ(R),is the graph whose vert ices are the non-zero zero-divisors of R、and w...Let R be an associative ring with identity and Z^*(K)be its set of non-zero zero-divisors.The undirected zero-divisor graph of R、denoted byΓ(R),is the graph whose vert ices are the non-zero zero-divisors of R、and where two distinct verticesγand s are adjacent if and only ifγs=0 or sγ=0.The dist ance bet ween vertices a and b is the length of the shortest path connecting them,and the diameter of the graph,diam(Γ(R)),is the superimum of these distances.In this paper,first we prove some results aboutΓ(R)of a semi-commutative ring R.Then,for a reversible ring R and a unique product monoid M、we prove 0≦diam(Γ(R))<diam(Γ(R[M]))≦3.We describe all the possibilities for the pair diam(Γ(R))and diam(Γ(R[M])),strictly in terms of the properties of a ring R,where K is a reversible ring and M is a unique product monoid.Moreover,an example showing the necessity of our assumptions is provided.展开更多
For a monoid M, we introduce M-McCoy rings, which are generalization of McCoy rings, and we investigate their properties. Every M-Armendariz ring is M-McCoy for any monoid M. We show that R is an M-McCoy ring if and o...For a monoid M, we introduce M-McCoy rings, which are generalization of McCoy rings, and we investigate their properties. Every M-Armendariz ring is M-McCoy for any monoid M. We show that R is an M-McCoy ring if and only if an n × n upper triangular matrix ring αUTn （R） over R is an M-McCoy ring for any monoid M. It is proved that if R is McCoy and R[x] is M-McCoy, then R[M] is McCoy for any monoid M. Moreover, we prove that if R is M-McCoy, then R[M] and R[x] are M-McCoy for a commutative and cancellative monoid M that contains an infinite cyclic submonoid.展开更多
基金Shandong Provincial Modern Agricultural Industrial Technology System:Project for Construction of Vegetation Innovative Team(SDAIT-05-18).
文摘This article describes the geographical indication characteristics of Zhuanbu strawberry,a special product of Yinan County,Shandong Province,a national geographical indication agricultural product,including specific production area,unique production environment,rich human history and unique product quality,summarizes the unique production method of Zhuanbu strawberry from selection of production area and varieties,production management,timely harvesting and other aspects,and puts forward corresponding industrial development measures,in order to maintain the brand of Zhuanbu strawberry to the greatest extent and further improve the brand awareness and market competitiveness of Zhuanbu strawberry.
文摘Let R be an associative ring with identity and Z^*(K)be its set of non-zero zero-divisors.The undirected zero-divisor graph of R、denoted byΓ(R),is the graph whose vert ices are the non-zero zero-divisors of R、and where two distinct verticesγand s are adjacent if and only ifγs=0 or sγ=0.The dist ance bet ween vertices a and b is the length of the shortest path connecting them,and the diameter of the graph,diam(Γ(R)),is the superimum of these distances.In this paper,first we prove some results aboutΓ(R)of a semi-commutative ring R.Then,for a reversible ring R and a unique product monoid M、we prove 0≦diam(Γ(R))<diam(Γ(R[M]))≦3.We describe all the possibilities for the pair diam(Γ(R))and diam(Γ(R[M])),strictly in terms of the properties of a ring R,where K is a reversible ring and M is a unique product monoid.Moreover,an example showing the necessity of our assumptions is provided.
基金the National Natural Science Foundation of China （No. 10171082） the Natural Science Foundation of Gansu Province （No. 3ZSA061-A25-015） and the Scientific Research Fund of Gansu Provincial Education Department （Nos. 06021-21 0410B-09）.
文摘For a monoid M, we introduce M-McCoy rings, which are generalization of McCoy rings, and we investigate their properties. Every M-Armendariz ring is M-McCoy for any monoid M. We show that R is an M-McCoy ring if and only if an n × n upper triangular matrix ring αUTn （R） over R is an M-McCoy ring for any monoid M. It is proved that if R is McCoy and R[x] is M-McCoy, then R[M] is McCoy for any monoid M. Moreover, we prove that if R is M-McCoy, then R[M] and R[x] are M-McCoy for a commutative and cancellative monoid M that contains an infinite cyclic submonoid.
