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PreprintarXiv licencearXiv

Prime Ideals and Projective Closure in the Boolean Polynomial Semiring

  • Tristan Bishop
  • Chris Eppolito
  • Radford Green
  • Jaiung Jun
  • Alex Norwood
  • Daisy Ivy Thackrah
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Abstract

In this paper, we investigate two related questions concerning the Boolean polynomial semiring in two variables. First, we study prime ideals in ๐”น[x,y], beginning with a complete classification of those generated by linear polynomials. Second, motivated by the limitations of ideals in capturing geometric phenomena over semirings, we introduce a notion of projective closure via congruences. We prove that this projective closure coincides with the topological closure in the projective space of prime congruences.

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Cite

BibTeXRIS
BibTeX
@misc{bishop2026prime,
  title = {{Prime Ideals and Projective Closure in the Boolean Polynomial Semiring}},
  author = {Tristan Bishop and Chris Eppolito and Radford Green and Jaiung Jun and Alex Norwood and Daisy Ivy Thackrah},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38657},
  eprint = {2609.38657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38657},
}
RIS
TY  - UNPB
TI  - Prime Ideals and Projective Closure in the Boolean Polynomial Semiring
AU  - Tristan Bishop
AU  - Chris Eppolito
AU  - Radford Green
AU  - Jaiung Jun
AU  - Alex Norwood
AU  - Daisy Ivy Thackrah
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38657
UR  - https://arxiv.org/abs/2609.38657
AB  - In this paper, we investigate two related questions concerning the Boolean polynomial semiring in two variables. First, we study prime ideals in ๐”น[x,y], beginning with a complete classification of those generated by linear polynomials. Second, motivated by the limitations of ideals in capturing geometric phenomena over semirings, we introduce a notion of projective closure via congruences. We prove that this projective closure coincides with the topological closure in the projective space of prime congruences.
ER  -