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Embedding of a Near-Ring into a Near-Ring with Identity
1987It is well known, that an arbitrary near-ring N may be embedded into a near-ring N with identity. Details and references are to be found, e.g., in [3; § 1, section c]. Also, it is very well known, that any ring A is an ideal of a ring A* with identity [2; p. 11].
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Mathematical Journal of Okayama University, 1990
Let \(N\) denote a zero-symmetric left near-ring, \(A\) a nonzero ideal of \(N\), and \(d\) a derivation on \(N\). The author proves several theorems on additive or multiplicative commutativity of \(N\), extending results of the reviewer and \textit{G. Mason} [Near-rings and near-fields, Proc. Conf., Tübingen, F.R.G. 1985, North-Holland Math. Stud. 137,
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Let \(N\) denote a zero-symmetric left near-ring, \(A\) a nonzero ideal of \(N\), and \(d\) a derivation on \(N\). The author proves several theorems on additive or multiplicative commutativity of \(N\), extending results of the reviewer and \textit{G. Mason} [Near-rings and near-fields, Proc. Conf., Tübingen, F.R.G. 1985, North-Holland Math. Stud. 137,
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Near-rings whose laminated near-rings are Boolean
九州大学教養部数学雑誌, 1987In [Proc. Edinb. Math. Soc., II. Ser. 23, 97-102 (1980; Zbl 0415.16028)] \textit{K. D. Magill, jun.} introduced the concept of a laminated near-ring. Let N be an arbitrary near-ring. Each element a in N yields a new near- ring \(N_ a\) whose additive group coincides with that of N and whose multiplication * is defined by \(x*y=xay\) for any two ...
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Polynomial and Matrix Near-Rings
Arabian Journal for Science and Engineering, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On derivations in near-rings and rings
Mathematical Journal of Okayama University, 1992In a near-ring \(R\) a derivation \(D\) is called an scp-derivation if \([x,y] = [D(x), D(y)]\), a Daif 1(2)-derivation if \(D(xy) - D(yx) = [x, y] (=[-x, y])\) (\(\forall x, y \in R\)). Various commutativity (and distributivity) results linked to such derivations are given: e.g.
Bell, Howard E., Mason, Gordon
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Boolean Orthogonalities For Near-rings
Results in Mathematics, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2009
A near-ring N is called an IFP near-ring provided that for all a, b, n ∈N, ab = 0 implies anb = 0. In this study, the IFP condition in a nearring is extended to the ideals in near-rings. If N/P is an IFP near-ring,where P is an ideal of a near-ring N, then we call P as the IFP-ideal ofN.
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A near-ring N is called an IFP near-ring provided that for all a, b, n ∈N, ab = 0 implies anb = 0. In this study, the IFP condition in a nearring is extended to the ideals in near-rings. If N/P is an IFP near-ring,where P is an ideal of a near-ring N, then we call P as the IFP-ideal ofN.
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