On maximal 𝑘-ideals of semirings

Sen, M. K.; Adhikari, M. R.

doi:10.1090/S0002-9939-1993-1132423-6

On maximal $k$-ideals of semirings
HTML articles powered by AMS MathViewer

by M. K. Sen and M. R. Adhikari PDF

Proc. Amer. Math. Soc. 118 (1993), 699-703 Request permission

Abstract:

For a semiring $S$ with commutative addition, conditions are considered such that $S$ has nontrivial $k$-ideals or maximal $k$-ideals, among others, by the help of the congruence class semiring $S/A$ defined by an ideal $A$ of $S$. Moreover, all maximal $k$-ideals of the semiring of nonnegative integers are described.

References

Samuel Bourne, The Jacobson radical of a semiring, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 163–170. MR 41827, DOI 10.1073/pnas.37.3.163
Samuel Bourne and Hans Zassenhaus, On the semiradical of a semiring, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 907–914. MR 97430, DOI 10.1073/pnas.44.9.907
L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864

Ideals in semirings with commutative addition

5

Kiyoshi Iséki, On ideals in semiring, Proc. Japan Acad. 34 (1958), 507–509. MR 100041
D. R. LaTorre, A note on quotient semirings, Proc. Amer. Math. Soc. 24 (1970), 463–465. MR 252451, DOI 10.1090/S0002-9939-1970-0252451-7
Hanns Joachim Weinert, Seminearrings, seminearfields and their semigroup-theoretical background, Semigroup Forum 24 (1982), no. 2-3, 231–254. MR 650573, DOI 10.1007/BF02572770