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k-zero-divisor hypergraphs of finite commutative rings |
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| รหัสดีโอไอ | |
| Title | k-zero-divisor hypergraphs of finite commutative rings |
| Creator | Pinkaew Siriwong |
| Contributor | Sajee Pianskool, Ratinan BoonKlurb |
| Publisher | Chulalongkorn University |
| Publication Year | 2559 |
| Keyword | Rings (Algebra), Hypergraphs, ริง (พีชคณิต), ไฮเพอร์กราฟ |
| Abstract | Let R be a commutative ring with nonzero identity and k ≥ 2 be a fixed integer. The k-zero-divisor hypergraph Hk(R) of R consists of the vertex set Z(R; k), the set of all k-zero-divisors of R, and the (hyper)edges of the form {α1, α2, α3, .... αk} where α1, α2, α3, ..., αk are k distinct elements in Z(R; k), which means (i) α1α2α3..., αk = 0 and (ii) the products of all elements of any (k - 1)- subsets of {α1, α2, α3, ..., αk} are nonzero. This thesis provides (i) a necessary con- dition of commutative rings that implies the completeness of their k-zero-divisor hypergraphs; (ii) a necessary condition of commutative rings that implies the abil- ity to partition their set of all k-zero-divisors into k partite sets and the complete- ness of that k-partite k-zero-divisor hypergraphs; and (iii) a necessary condition of commutative rings that implies the ability to partition their set of all -zero- divisors into k partite sets, for some integer σ ≥ k. Moreover, the diameter and the minimum length of all cycles of those hypergraphs are determined. |
| URL Website | cuir.car.chula.ac.th |
