About multiplicatively idempotent semirings with annihilator properties
https://doi.org/10.26907/2949-3919.2024.4.24-34
Abstract
We study one class of semirings close to distributive lattices, namely: semirings with commutative idempotent multiplication, satisfying the identity x + 2xy = x. For such semirings, the equalizing properties are investigated (Theorems 7, 8, 10, Proposition 12). The results obtained can be applied to distributive lattices (Propositions 15, 16, 17). The work provides examples and explanatory notes.
Keywords
multiplicatively idempotent semiring,
distributive lattice,
equalizing condition,
annihilator condition,
equalizing property
Supporting agencies: The work is supported by the Russian Science Foundation (grant no. 24-21-00117).
About the Author
E. M. Vechtomov
Vyatka State University
Russian Federation
Russian Federation
Evgenii Mikhailovich Vechtomov
36 Moskovskay str., Kirov 610000
References
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Review
For citations:
Vechtomov E.M. About multiplicatively idempotent semirings with annihilator properties. Mathematics and Theoretical Computer Science. 2024;2(4):24-34. (In Russ.) https://doi.org/10.26907/2949-3919.2024.4.24-34
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