TY - JOUR
T1 - Ideals of polynomial semirings in tropical mathematics
AU - Izhakian, Zur
AU - Rowen, Louis
N1 - Funding Information:
This work has been supported by the Israel Science Foundation grant No. 448/09.
PY - 2013/3
Y1 - 2013/3
N2 - We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from layered varieties, for which we prove that every prime ideal is a consequence of finitely many binomials. We also obtain layered tropical versions of the classical Principal Ideal Theorem and Hilbert Basis Theorem.
AB - We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from layered varieties, for which we prove that every prime ideal is a consequence of finitely many binomials. We also obtain layered tropical versions of the classical Principal Ideal Theorem and Hilbert Basis Theorem.
KW - Hilbert Basis Theorem
KW - Noetherian ideal theory
KW - Principal Ideal Theorem
KW - Tropical and supertropical algebra
KW - layered algebra
KW - layered ideals
UR - http://www.scopus.com/inward/record.url?scp=84872439521&partnerID=8YFLogxK
U2 - 10.1142/S0219498812501435
DO - 10.1142/S0219498812501435
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AN - SCOPUS:84872439521
SN - 0219-4988
VL - 12
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 2
M1 - 1250143
ER -