Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n^4 elements and these rings have five (2p+4) isomorphic classes for p =...Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n^4 elements and these rings have five (2p+4) isomorphic classes for p = 2 (p p 2).展开更多
In 1967, K. Koh showed that (Ⅰ)if a ring R contains n (n】1) left (right)zero divi-sors, then |R|≤n^2; (Ⅱ)if a ring R contains n (n】1)left (right)zero divisors, and it has an identity and |R|=n^2, then n is a powe...In 1967, K. Koh showed that (Ⅰ)if a ring R contains n (n】1) left (right)zero divi-sors, then |R|≤n^2; (Ⅱ)if a ring R contains n (n】1)left (right)zero divisors, and it has an identity and |R|=n^2, then n is a power of a prime p, and every minimal right ideal I of R necessarily satisfies I^2=0. In fact, if a ring R contains one-sided zero divisors, then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 paper, we obtain the period of generalized Fibonacci sequence in finite rings with identity of order p2 by using equality recursively defined by Fn＋2 = A1Fn＋1 ＋ A0Fn, for n ≥ 0, where F0 = 0 （ the zero of...In this paper, we obtain the period of generalized Fibonacci sequence in finite rings with identity of order p2 by using equality recursively defined by Fn＋2 = A1Fn＋1 ＋ A0Fn, for n ≥ 0, where F0 = 0 （ the zero of the ring）, F1 = 1 （the identity of the ring） and A0 , A1 are generators elements of finite rings with identity of order p2. Also, we get some results between the period of generalized Fibonacci sequence in the finite rings oforderp2 and characteristic of these rings.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.
文摘Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n^4 elements and these rings have five (2p+4) isomorphic classes for p = 2 (p p 2).
文摘In 1967, K. Koh showed that (Ⅰ)if a ring R contains n (n】1) left (right)zero divi-sors, then |R|≤n^2; (Ⅱ)if a ring R contains n (n】1)left (right)zero divisors, and it has an identity and |R|=n^2, then n is a power of a prime p, and every minimal right ideal I of R necessarily satisfies I^2=0. In fact, if a ring R contains one-sided zero divisors, then
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 paper, we obtain the period of generalized Fibonacci sequence in finite rings with identity of order p2 by using equality recursively defined by Fn＋2 = A1Fn＋1 ＋ A0Fn, for n ≥ 0, where F0 = 0 （ the zero of the ring）, F1 = 1 （the identity of the ring） and A0 , A1 are generators elements of finite rings with identity of order p2. Also, we get some results between the period of generalized Fibonacci sequence in the finite rings oforderp2 and characteristic of these rings.
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.
