SIFAT-SIFAT SEMIRING DAN KONSTRUKSINYA

Authors

  • Ana Rahmawati Universitas Pesantren Tinggi Darul „Ulum (Unipdu) Jombang

DOI:

https://doi.org/10.25273/jems.v1i2.145

Keywords:

semiring, hasil kali langsung semiring, latis distributif, aljabar Boole, semiring polinom atas semiring.

Abstract

Semiring didefinisikan sebagai himpunan tak kosong dengan dua operasi biner (penjumlahan dan perkalian). Di bawah operasi penjumlahan semiring merupakan monoid komutatif, dan dibawah operasi perkalian merupakan semigrup, serta berlakunya sifat distributif perkalian terhadap penjumlahan (distributif kiri dan kanan). Seperti sruktur ring, dalam semiring juga dikenal beberapa substruktur dan sifat-sifat serupa yang meliputi ideal; pembagi nol; invers; elemen identitas dan homomorfisme. Semiring dapat dikonstruksi dari hasil kali langsung semiring dengan operasi per-komponen dan latis distributif. Selanjutnya semiring yang dibangun dari aljabar Boole mhingga dengan kardinalitas lebih dari dua merupakan semiring ketat, komutatif dengan kesatuan dan mempunyai pembagi nol. Pada bagian akhir, juga akan disajikan bahwa himpunan polinom dapat membentuk semiring polinom dengan operasi pada polinom.

 

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Published

2016-12-19

Issue

Vol. 1 No. 2 (2013)

Section

Articles

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