Results 281 to 290 of about 93,518 (299)
Some of the next articles are maybe not open access.
NEW KINDS OF NEAR-RINGS FROM OLD NEAR RINGS
JP Journal of Algebra, Number Theory and Applications, 2018Summary: In this paper, we construct that a new kind of near-ring, that is, \((e, t)\)-near-ring \((R, +,\ast)\) with given addition in \(R\) and new multiplication \(\ast\) which is expressed in terms of the original multiplication and addition by defining \(a\ast b\) to be a polynomial in \(a\) and \(b\), from a given near-ring \((R, +, \cdot ...
openaire +2 more sources
Centralizer Near-rings, Matrix Near-rings and Cyclic p-Groups
Algebra Colloquium, 2005If G is a finite group and [Formula: see text] is a group of automorphisms of G, then it is known that the matrix near-ring [Formula: see text] is a subnear-ring of the centralizer near-ring [Formula: see text] for every m ≥ 2. Conditions are known under which [Formula: see text] is a proper subnear-ring of [Formula: see text], and if [Formula: see ...
Smith, Kirby C., van Wyk, Leon
openaire +2 more sources
2021
Summary: In this paper, the authors have defined the valuation near ring. They have proved some theorem, for example, they have shown every valuation near ring is a local near ring and the ideals of \(N\) are totally ordered by inclusion. Also, the symbol valuation \(N\)-group in near rings has been introduced. Finally, every valuation \(N\)-group is a
Khodadadpour, E., Roodbarylor, T.
openaire +2 more sources
Summary: In this paper, the authors have defined the valuation near ring. They have proved some theorem, for example, they have shown every valuation near ring is a local near ring and the ideals of \(N\) are totally ordered by inclusion. Also, the symbol valuation \(N\)-group in near rings has been introduced. Finally, every valuation \(N\)-group is a
Khodadadpour, E., Roodbarylor, T.
openaire +2 more sources
Canadian Journal of Mathematics, 1969
The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
openaire +2 more sources
The following results (9, Exercise 26, p. 10; 1, Theorem 9.2; 8, Theorem III. 1.11) are known.(A) Let R be a ring with more than one element. Then R is a division ring ifand only if for every a ≠0 in R, there exists a unique b in R such that aba = a.(B) Let R be a near-ring which contains a right identity e ≠ 0.
openaire +2 more sources
Planar Near-Rings, Sandwich Near-Rings and Near-Rings with Right Identity
2005We show that every near-ring containing a multiplicative right identity can be described as a centralizer near-ring with sandwich multiplication. Using this result we characterize planar near-rings and near-rings solving the equation xa=c in terms of such centralizer near-rings with sandwich multiplication.
openaire +1 more source
1987
The principal theorem states that a finite non-constant near-ring N is geometric if and only if it is strongly monogenic. This provides the basis for a well-defined representation of the group space on the group \(\{Z\to aZ+b| \quad a,b\in N,\quad a\neq 0\}\) acting on the underlying set of N.
openaire +4 more sources
The principal theorem states that a finite non-constant near-ring N is geometric if and only if it is strongly monogenic. This provides the basis for a well-defined representation of the group space on the group \(\{Z\to aZ+b| \quad a,b\in N,\quad a\neq 0\}\) acting on the underlying set of N.
openaire +4 more sources
1997
Not much work has been done on composition near-rings. Here we initiate such investigations. Amongst others we give construction techniques for double composition near-rings and we give two non-isomorphic Peirce decompositions for a composition near-ring (using both the multiplication and composition).
Quentin N. Petersen, Stefan Veldsman
openaire +1 more source
Not much work has been done on composition near-rings. Here we initiate such investigations. Amongst others we give construction techniques for double composition near-rings and we give two non-isomorphic Peirce decompositions for a composition near-ring (using both the multiplication and composition).
Quentin N. Petersen, Stefan Veldsman
openaire +1 more source
1992
A near-ring \(N\) is called \(N\)-simple if it has no proper \(N\)-subgroups; it is called \(A\)-simple if it has no \(N\)-subgroups \(H\) such that \(HN=\{0\}\). The radical \(J_ 2(N)\) of a zero-symmetric ring \(N\) with an invariant series whose factors are \(N\)-simple is nilpotent; moreover the factor \(N/J_ 2(N)\) is a direct sum of \(A\)-simple ...
BENINI, Anna, PELLEGRINI, Silvia
openaire +4 more sources
A near-ring \(N\) is called \(N\)-simple if it has no proper \(N\)-subgroups; it is called \(A\)-simple if it has no \(N\)-subgroups \(H\) such that \(HN=\{0\}\). The radical \(J_ 2(N)\) of a zero-symmetric ring \(N\) with an invariant series whose factors are \(N\)-simple is nilpotent; moreover the factor \(N/J_ 2(N)\) is a direct sum of \(A\)-simple ...
BENINI, Anna, PELLEGRINI, Silvia
openaire +4 more sources
1987
Abstract In this paper we introduce a partial order relation in a reduced near-ring and show that the set of all idempotents of a reduced near-ring with identity forms a Boolean algebra under this partial ordering. Further we introduce the notions hyper atom and orthogonal subsets in a reduced near-ring with identity and show that a reduced near-ring
D. Ramakotaiah, V. Sambasivarao
openaire +1 more source
Abstract In this paper we introduce a partial order relation in a reduced near-ring and show that the set of all idempotents of a reduced near-ring with identity forms a Boolean algebra under this partial ordering. Further we introduce the notions hyper atom and orthogonal subsets in a reduced near-ring with identity and show that a reduced near-ring
D. Ramakotaiah, V. Sambasivarao
openaire +1 more source