Matches in SemOpenAlex for { <https://semopenalex.org/work/W2002257546> ?p ?o ?g. }
Showing items 1 to 56 of
56
with 100 items per page.
- W2002257546 endingPage "226" @default.
- W2002257546 startingPage "208" @default.
- W2002257546 abstract "The purpose of this article is to present the idea of coloring of a commutative ring. This idea establishes a connection between graph theory and commutative ring theory which hopefully will turn out to be mutually beneficial for these two branches of mathemathics. In this introductory paper we shall mainly be interested in characterizing and discussing the rings which are finitely colorable, leaving aside, for the moment, possible applications to graph theory. Let R be a commutative ring. We consider R as a simple graph whose vertices are the elements of R, such that two different elements x and y are adjacent iff xy = 0. We let x(R) denote the chromatic number of the graph, i.e., the minimal number of colors which can be assigned to the elements of R in such a way that every two adjacent elements have different colors. A subset C = (xi, . . . . x,} is called a clique provided xixj = 0 for all i # j. If R contains a clique with n elements, and every clique has at most y1 elements, we say that the clique number of R is n and write clique R = n. If the sizes of the cliques in R are not bounded we define clique R = co. We shall show that clique R = co actually entails the existence of an infinite clique. Obviously x(R) 3 clique R and for general graph G we certainly may have x(G) > clique G. However, in the case of commutative rings we have not found any example where x(R) > clique R. The lack of such counterexamples together with the fact that we have been able to establish the equality x(R) = clique R for certain (rather wide) classes of rings like reduced and principal ideal rings motivates the following conjecture." @default.
- W2002257546 created "2016-06-24" @default.
- W2002257546 creator A5068095716 @default.
- W2002257546 date "1988-07-01" @default.
- W2002257546 modified "2023-10-17" @default.
- W2002257546 title "Coloring of commutative rings" @default.
- W2002257546 cites W1982373193 @default.
- W2002257546 cites W600072479 @default.
- W2002257546 doi "https://doi.org/10.1016/0021-8693(88)90202-5" @default.
- W2002257546 hasPublicationYear "1988" @default.
- W2002257546 type Work @default.
- W2002257546 sameAs 2002257546 @default.
- W2002257546 citedByCount "882" @default.
- W2002257546 countsByYear W20022575462012 @default.
- W2002257546 countsByYear W20022575462013 @default.
- W2002257546 countsByYear W20022575462014 @default.
- W2002257546 countsByYear W20022575462015 @default.
- W2002257546 countsByYear W20022575462016 @default.
- W2002257546 countsByYear W20022575462017 @default.
- W2002257546 countsByYear W20022575462018 @default.
- W2002257546 countsByYear W20022575462019 @default.
- W2002257546 countsByYear W20022575462020 @default.
- W2002257546 countsByYear W20022575462021 @default.
- W2002257546 countsByYear W20022575462022 @default.
- W2002257546 countsByYear W20022575462023 @default.
- W2002257546 crossrefType "journal-article" @default.
- W2002257546 hasAuthorship W2002257546A5068095716 @default.
- W2002257546 hasConcept C161491579 @default.
- W2002257546 hasConcept C183778304 @default.
- W2002257546 hasConcept C202444582 @default.
- W2002257546 hasConcept C33923547 @default.
- W2002257546 hasConceptScore W2002257546C161491579 @default.
- W2002257546 hasConceptScore W2002257546C183778304 @default.
- W2002257546 hasConceptScore W2002257546C202444582 @default.
- W2002257546 hasConceptScore W2002257546C33923547 @default.
- W2002257546 hasIssue "1" @default.
- W2002257546 hasLocation W20022575461 @default.
- W2002257546 hasOpenAccess W2002257546 @default.
- W2002257546 hasPrimaryLocation W20022575461 @default.
- W2002257546 hasRelatedWork W1954846941 @default.
- W2002257546 hasRelatedWork W1975068388 @default.
- W2002257546 hasRelatedWork W1977914655 @default.
- W2002257546 hasRelatedWork W1986264951 @default.
- W2002257546 hasRelatedWork W2043897844 @default.
- W2002257546 hasRelatedWork W2061776474 @default.
- W2002257546 hasRelatedWork W2071709946 @default.
- W2002257546 hasRelatedWork W2107434903 @default.
- W2002257546 hasRelatedWork W3199852337 @default.
- W2002257546 hasRelatedWork W4230039479 @default.
- W2002257546 hasVolume "116" @default.
- W2002257546 isParatext "false" @default.
- W2002257546 isRetracted "false" @default.
- W2002257546 magId "2002257546" @default.
- W2002257546 workType "article" @default.