Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditi...Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.展开更多
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K...The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.展开更多
Some results on RaRb transformation of compound finite automata over finite field are generalized to the case of commutative rings. Properties of RaRb transformation are discussed and applied to the inversion problem ...Some results on RaRb transformation of compound finite automata over finite field are generalized to the case of commutative rings. Properties of RaRb transformation are discussed and applied to the inversion problem for compound finite automata.展开更多
Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1&#...Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1×R2×…×Rn(each Ri is local for i=1,2,3,...,n),we also give algebraic characterizations of the ring R when the clique number of Γ(R)is four.展开更多
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta...In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.展开更多
We study the algebraic structure of rings R whose zero-divisor graph T(R)has clique number four.Furthermore,we give complete characterizations of all the finite commutative local rings with clique number 4.
In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacen...In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacent if and only if xy=0 or x+y∈Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.展开更多
Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutat...Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.展开更多
文摘Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.
文摘The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.
文摘Some results on RaRb transformation of compound finite automata over finite field are generalized to the case of commutative rings. Properties of RaRb transformation are discussed and applied to the inversion problem for compound finite automata.
基金This research was supported by the National Natural Science Foundation of China(No.11801356,No.11401368,No.11971338)by the Natural Science Foundation of Shanghai(No.19ZR1424100).
文摘Let R be a commutative ring and Γ(R)be its zero-divisor graph.We completely determine the structure of all finite commutative rings whose zero-divisor graphs have clique number one,two,or three.Furthermore,if R■R1×R2×…×Rn(each Ri is local for i=1,2,3,...,n),we also give algebraic characterizations of the ring R when the clique number of Γ(R)is four.
文摘In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.
基金This research was supported by the National Natural Science Foundation of China(No.11801356,No.11401368,No.11971338)by the Natural Science Foundation of Shanghai(No.19ZR1424100).
文摘We study the algebraic structure of rings R whose zero-divisor graph T(R)has clique number four.Furthermore,we give complete characterizations of all the finite commutative local rings with clique number 4.
文摘In this paper,we introduce a new graph whose vertices are the non-zero zerodivisors of a commutativc ring R、and for distincts elements x and y in the set Z(R)^(*)of the non-zero zero-divisors of R,x and y are adjacent if and only if xy=0 or x+y∈Z(R).We present some properties and examples of this graph,and we study its relationship with the zero-divisor graph and with a subgraph of the total graph of a commutative ring.
基金Supported by the Anhui Provincial Key Natural Science Foundation of Universities and Colleges (Grant No.KJ2007A127ZC)
文摘Polynomial functions （in particular, permutation polynomials） play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors.
