Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive ...Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive laws does not hold in general. We introduce two ways in which matrix near-rings can be defined and discuss the structure of each. One is as given by Beildeman and the other is as defined by Meldrum. Beildeman defined his matrix near-rings as normal arrays under the operation of matrix multiplication and addition. He showed that we have a matrix near-ring over a near-ring if, and only if, it is a ring. In this case it is not possible to obtain a matrix near-ring from a proper near-ring. Later, in 1986, Meldrum and van der Walt defined matrix near-rings over a near-ring as mappings from the direct sum of n copies of the additive group of the near-ring to itself. In this case it can be shown that a proper near-ring is obtained. We prove several properties, introduce some special matrices and show that a matrix notation can be introduced to make calculations easier, provided that n is small.展开更多
The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（...The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.展开更多
With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of...With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.展开更多
In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained d...In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained derivation d satisfying the condition that d（a） is not a left zero-divisor in R for some a ∈ R. As consequences, we generalize several commutativity theorems for 3-prime near-rings admitting derivations.展开更多
Let N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N o...Let N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N or D（[x,y]） = -xk[x,y]xI for all x,y ∈ N, then N is a commutative ring. （2） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（x o y） = xk（x o y）xl for all x, y ∈ N or D（x o y） = -xk（x o y）xl for all x, y ∈ N, then N is a commutative ring. Moreover, some interesting relations between the prime graph and zero-divisor graph of N are studied.展开更多
Nowadays some promising authenticated group key agreement protocols are constructed on braid groups, dynamic groups, pairings and bilinear pairings. Hence the non-abelian structure has attracted cryptographers to cons...Nowadays some promising authenticated group key agreement protocols are constructed on braid groups, dynamic groups, pairings and bilinear pairings. Hence the non-abelian structure has attracted cryptographers to construct public-key cryptographic protocols. In this article, we propose a new authenticated group key agreement protocol which works in non-abelian near-rings. We have proved that our protocol meets the security attributes under the assumption that the twist conjugacy search problem（TCSP） is hard in near-ring.展开更多
给出(∈,∈∨q(λ,μ))-模糊子近环和理想的全新概念及刻画,并获得一些充分必要条件。其中值得指出的是当λ=0,μ=0.5时可以得到Davvaz文章中的相关结论[B.Davvaz,(∈,∈∨q)-fuzzysubnear-rings and ideals,soft comput.,2006,10:206-2...给出(∈,∈∨q(λ,μ))-模糊子近环和理想的全新概念及刻画,并获得一些充分必要条件。其中值得指出的是当λ=0,μ=0.5时可以得到Davvaz文章中的相关结论[B.Davvaz,(∈,∈∨q)-fuzzysubnear-rings and ideals,soft comput.,2006,10:206-211]。当λ=0,μ=1时可以得到Rosenfeld意义下的结论。展开更多
文摘Matrix rings are prominent in abstract algebra. In this paper we give an overview of the theory of matrix near-rings. A near-ring differs from a ring in that it does not need to be abelian and one of the distributive laws does not hold in general. We introduce two ways in which matrix near-rings can be defined and discuss the structure of each. One is as given by Beildeman and the other is as defined by Meldrum. Beildeman defined his matrix near-rings as normal arrays under the operation of matrix multiplication and addition. He showed that we have a matrix near-ring over a near-ring if, and only if, it is a ring. In this case it is not possible to obtain a matrix near-ring from a proper near-ring. Later, in 1986, Meldrum and van der Walt defined matrix near-rings over a near-ring as mappings from the direct sum of n copies of the additive group of the near-ring to itself. In this case it can be shown that a proper near-ring is obtained. We prove several properties, introduce some special matrices and show that a matrix notation can be introduced to make calculations easier, provided that n is small.
基金Supported by the National Natural Science Foundation of China (60875034)the Natural Science Foundationof Education Committee of Hubei Province (D20092901+3 种基金Q20092907D20082903B200529001)the NaturalScience Foundation of Hubei Province (2008CDB341)
文摘The concept of（∈,∈∨q）-fuzzy subnear-rings（ideals） of a near-ring is introduced and some of its related properties are investigated.In particular,the relationships among ordinary fuzzy subnear-rings（ideals）,（∈,∈∨ q）-fuzzy subnear-rings（ideals） and（∈,∈∨q）-fuzzy subnear-rings（ideals） of near-rings are described.Finally,some characterization of [μ]t is given by means of（∈,∈∨ q）-fuzzy ideals.
基金Supported by the National Natural Science Foundation of China(60875034)the Natural Science Foundation of Education Committee of Hubei Province(D20092901),the Natural Science Foundation of Hubei Province(2009CDB340)
文摘With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.
文摘In this paper we first prove that a near-ring admits a derivation if and only if it is zero-symmetric. Also, we prove some commutativity theorems for a non-necessarily 3-prime near-ring R with a suitably-constrained derivation d satisfying the condition that d（a） is not a left zero-divisor in R for some a ∈ R. As consequences, we generalize several commutativity theorems for 3-prime near-rings admitting derivations.
文摘Let N be a prime near-ring. We show two main results on the commutativity of N： （1） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（[x,y]） = xk[x,y]xl for all x,y ∈ N or D（[x,y]） = -xk[x,y]xI for all x,y ∈ N, then N is a commutative ring. （2） If there exist k, l ∈ N such that N admits a generalized derivation D satisfying either D（x o y） = xk（x o y）xl for all x, y ∈ N or D（x o y） = -xk（x o y）xl for all x, y ∈ N, then N is a commutative ring. Moreover, some interesting relations between the prime graph and zero-divisor graph of N are studied.
文摘Nowadays some promising authenticated group key agreement protocols are constructed on braid groups, dynamic groups, pairings and bilinear pairings. Hence the non-abelian structure has attracted cryptographers to construct public-key cryptographic protocols. In this article, we propose a new authenticated group key agreement protocol which works in non-abelian near-rings. We have proved that our protocol meets the security attributes under the assumption that the twist conjugacy search problem（TCSP） is hard in near-ring.
文摘给出(∈,∈∨q(λ,μ))-模糊子近环和理想的全新概念及刻画,并获得一些充分必要条件。其中值得指出的是当λ=0,μ=0.5时可以得到Davvaz文章中的相关结论[B.Davvaz,(∈,∈∨q)-fuzzysubnear-rings and ideals,soft comput.,2006,10:206-211]。当λ=0,μ=1时可以得到Rosenfeld意义下的结论。
