Geodesic
On the sheaf representation of a $pq$-Baer $*$-semiring with involution
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 190-202
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In the paper, a functional (sheaf) representation of a $pq$-Baer $*$-semiring with involution is obtained. For a $*$-semiring, the notions of central and central prime ideals are introduced. The set ${\rm Sp}\,S$ of all central prime ideals of a $pq$-Baer $*$-semiring with the Zariski topology becomes a zero-dimensional compact Hausdorff space. The sheaf $(\mathbb{L}(S), {\rm Sp}\,S)$ of $*$-semirings is constructed on ${\rm Sp}\,S$ as a basis space. It is proved that an arbitrary $pq$-Baer $*$-semiring is $*$-isomorphic to the $*$-semiring of all global sections of the sheaf $\mathbb{L}(S)$. Open questions are formulated.
Keywords: semiring with involution, $pq$-Baer $*$-semiring, sheaf representation. 
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N. S. Protasov; V. V. Chermnykh. On the sheaf representation of a $pq$-Baer $*$-semiring with involution. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 190-202. http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a13/

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