The characterization of regular hemirings.
A hemiring is an algebra \((S,+,\cdot)\) which has all the properties of a ring except that \((S,+)\) is a commutative semigroup (with zero) rather than a commutative group. A left ideal \(A\) of a hemiring \(S\) is called left \(h\)-ideal if for \(\forall x,z\in S\), \(\forall a,b\in A\) from \(x+a+z=b+z\) follows \(x\in A\). A fuzzy subset \(\mu\colon S\to [0,1]\) of a hemiring \(S\) is called fuzzy \(h\)-bi-ideal if for \(\forall x,y,z,a,b\in S\) holds \(\mu(x+y)\geq\min(\mu(x),\mu(y))\), \(\mu(xy)\geq\min(\mu(x),\mu(y))\), \(\mu(xyz)\geq\min(\mu(x),\mu(z))\) and \(x+a+z=b+z\Rightarrow\mu(x)\geq\min(\mu(a),\mu(b))\). A hemiring \(S\) is called \(h\)-hemiregular if \((\forall x\in S)(\exists a,a',z\in S)(x+xax+z=xa'x+z)\). Here are investigated properties of fuzzy \(h\)-bi-ideals, fuzzy \(h\)-quasi-ideals and \(h\)-hemiregular hemirings; the paper contains some misprints.
scientific article; zbMATH DE number 5669439