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Afrika Matematika, 2014
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Dutta, T. K., Kar, S., Das, K.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dutta, T. K., Kar, S., Das, K.
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Monatshefte f?r Mathematik, 2002
A \(^*\)-semiring is an additively commutative semiring \((S,+,\cdot)\) with absorbing zero and identity 1 equipped with a star operation \(^*\colon S\to S\). If \((x+y)^*=(x^*y)^*x^*\) and \((xy)^*=1+x(yx)^*y\) for all \(x,y\in S\) then \((S,+,\cdot)\) is called a Conway semiring.
Ésik, Z., Kuich, W.
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A \(^*\)-semiring is an additively commutative semiring \((S,+,\cdot)\) with absorbing zero and identity 1 equipped with a star operation \(^*\colon S\to S\). If \((x+y)^*=(x^*y)^*x^*\) and \((xy)^*=1+x(yx)^*y\) for all \(x,y\in S\) then \((S,+,\cdot)\) is called a Conway semiring.
Ésik, Z., Kuich, W.
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ARMENDARIZ AND QUASI-ARMENDARIZ SEMIRINGS AND PS SEMIRINGS
Asian-European Journal of Mathematics, 2011In this paper we extend some results of ([2], [11], [12], [13], [15]) for non commutative semirings with identity 1 ≠ 0. We prove the following theorems: (1) Let R be a CN-semiring such that 0 is a P-primary ideal of R and P2 = 0. Then R is a quasi-Armendariz semiring.
Gupta, Vishnu, Kumar, Pramod
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Journal of Mathematical Sciences, 2006
In classical ring theory there are many results containing different algebraic conditions which force an arbitrary ring to be a full matrix ring. This paper deals with similar conditions which force a semiring \(S\) to be a matrix semiring over some different semiring \(R\).
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In classical ring theory there are many results containing different algebraic conditions which force an arbitrary ring to be a full matrix ring. This paper deals with similar conditions which force a semiring \(S\) to be a matrix semiring over some different semiring \(R\).
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on O-simple semirings, semigroup semirings, and two kinds of division semirings
Semigroup Forum, 1984In this paper we consider O-simple semirings S, where O denotes the multiplicative zero of S, which may be in particular the additive neutral o of S at the same time. In this context we give some statements on matrix semirings and introduce contracted semigroup semirings in §3, a matter of interest of its own.
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1999
Many of the semirings originally studied, such as ℕ and ideal(R), have a partial-order structure in addition to their algebraic structure and, indeed, the most interesting theorems concerning them make use of the interplay between these two structures.
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Many of the semirings originally studied, such as ℕ and ideal(R), have a partial-order structure in addition to their algebraic structure and, indeed, the most interesting theorems concerning them make use of the interplay between these two structures.
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Semiring-valued Ideals in Semirings and Rings
1999Let (R, +,·) and (S, ⊕, ⊙) be semirings. An R-valued left [resp. right] ideal of S is a R-valued subsemigroup f of (S, ⊕) which is not a constant function and which satisfies the following additional condition: $$f\left( {s' \odot s} \right) \geqslant f\left( s \right)\left[ {resp.\,f\left( {s \odot s'} \right) \geqslant f\left( s \right)} \right]\,
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