Results 221 to 230 of about 249,087 (268)
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Canadian Mathematical Bulletin, 1969
In this paper we introduce the concept of Boolean near-rings. Using any Boolean ring with identity, we construct a class of Boolean near-rings, called special, and determine left ideals, ideals, factor near-rings which are Boolean rings, isomorphism classes, and ideals which are near-ring direct summands for these special Boolean near-rings.Blackett [6]
Clay, James R., Lawver, Donald A.
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In this paper we introduce the concept of Boolean near-rings. Using any Boolean ring with identity, we construct a class of Boolean near-rings, called special, and determine left ideals, ideals, factor near-rings which are Boolean rings, isomorphism classes, and ideals which are near-ring direct summands for these special Boolean near-rings.Blackett [6]
Clay, James R., Lawver, Donald A.
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Archiv der Mathematik, 1986
Until this article, there has not been an acceptable approach to the concept of a near-ring of matrices over an arbitrary near-ring. The authors overcome the inherent problems associated with arrays and are motivated by the fact that for a ring, each matrix represents an endomorphism of \((R^ n,+)\) and as such it is derived from the endomorphisms of ...
Meldrum, J. D. P. +1 more
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Until this article, there has not been an acceptable approach to the concept of a near-ring of matrices over an arbitrary near-ring. The authors overcome the inherent problems associated with arrays and are motivated by the fact that for a ring, each matrix represents an endomorphism of \((R^ n,+)\) and as such it is derived from the endomorphisms of ...
Meldrum, J. D. P. +1 more
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Canadian Mathematical Bulletin, 1968
Blackett [4] introduced the concepts of near-ring homomorphism and near-ring ideal. Beidleman [1] established the fundamental homomorphism theorem and the isomorphism theorems for (left) near - rings obeying the condition that 0.a = 0 for every a in the near-ring. Several others, for example [3], [5], and [7], have taken up the study of ideals.
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Blackett [4] introduced the concepts of near-ring homomorphism and near-ring ideal. Beidleman [1] established the fundamental homomorphism theorem and the isomorphism theorems for (left) near - rings obeying the condition that 0.a = 0 for every a in the near-ring. Several others, for example [3], [5], and [7], have taken up the study of ideals.
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New Mathematics and Natural Computation, 2019
In this paper, we consider the problem of how to define [Formula: see text]-nearness ring in the sense of Nobusawa theory which extends the notion of a nearness ring and [Formula: see text]-rings [N. Nobusawa, Osaka J. Math. 1 (1964) 81–89; M. A. Öztürk and E. İnan, Annals of Fuzzy Mathematics and Informatics 17(2) (2019) 115–131].
Mehmet Ali Öztürk, Young Bae Jun
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In this paper, we consider the problem of how to define [Formula: see text]-nearness ring in the sense of Nobusawa theory which extends the notion of a nearness ring and [Formula: see text]-rings [N. Nobusawa, Osaka J. Math. 1 (1964) 81–89; M. A. Öztürk and E. İnan, Annals of Fuzzy Mathematics and Informatics 17(2) (2019) 115–131].
Mehmet Ali Öztürk, Young Bae Jun
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Archiv der Mathematik, 2002
Let \(R\) be a left near-ring and let \(E(R^+)\) be the monoid of endomorphisms of \((R,+)\). For each \(a\in R\), let \(a_\ell\colon R\to R\) be the left-multiplication map \(x\mapsto ax\) and note that \(a_\ell\in E(R^+)\). Let \(L\colon R\to E(R^+)\) be defined by \(L(a)=a_\ell\), and call \(R\) an \(E\)-near-ring if \(L\) is a bijection.
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Let \(R\) be a left near-ring and let \(E(R^+)\) be the monoid of endomorphisms of \((R,+)\). For each \(a\in R\), let \(a_\ell\colon R\to R\) be the left-multiplication map \(x\mapsto ax\) and note that \(a_\ell\in E(R^+)\). Let \(L\colon R\to E(R^+)\) be defined by \(L(a)=a_\ell\), and call \(R\) an \(E\)-near-ring if \(L\) is a bijection.
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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.
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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.
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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.
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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.
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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.
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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
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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 ...
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