FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1988672308> ?p ?o ?g. }

• W1988672308 abstract "Kaplanski's Zero Divisor Conjecture envisions that for a torsion-free group G and an integral domain R, the group ring R[G] does not contain non-trivial zero divisors. We define the length of an element a in R[G] as the minimal non-negative integer k for which there are ring elements r_1,...,r_k in R and group elements g_1,...,g_k in G such that a = r_1 g_1+...+r_k g_k. We investigate the conjecture when R is the field of rational numbers. By a reduction to the finite field with two elements, we show that if ab = 0 for non-trivial elements in the group ring of a torsion-free group over the rationals, then the lengths of a and b cannot be among certain combinations. More precisely, we show for various pairs of integers (i,j) that if one of the lengths is at most i then the other length must exceed j. Using combinatorial arguments we show this for the pairs (3,6) and (4,4). With a computer-assisted approach we strengthen this to show the statement holds for the pairs (3,16) and (4,7). As part of our method, we describe a combinatorial structure, which we call matched rectangles, and show that for these a canonical labeling can be computed in quadratic time. Each matched rectangle gives rise to a presentation of a group. These associated groups are universal in the sense that there is no counterexample to the conjecture among them if and only if the conjecture is true over the rationals." @default.
• W1988672308 created "2016-06-24" @default.
• W1988672308 creator A5017685495 @default.
• W1988672308 date "2012-02-29" @default.
• W1988672308 modified "2023-09-27" @default.
• W1988672308 title "On Zero Divisors with Small Support in Group Rings of Torsion-Free Groups" @default.
• W1988672308 cites W135919544 @default.
• W1988672308 cites W1590608466 @default.
• W1988672308 cites W1594873819 @default.
• W1988672308 cites W1596519874 @default.
• W1988672308 cites W1986291064 @default.
• W1988672308 cites W1987977346 @default.
• W1988672308 cites W1999227640 @default.
• W1988672308 cites W1999677424 @default.
• W1988672308 cites W2001950484 @default.
• W1988672308 cites W2002096572 @default.
• W1988672308 cites W201685787 @default.
• W1988672308 cites W2043055027 @default.
• W1988672308 cites W2068945870 @default.
• W1988672308 cites W2070964129 @default.
• W1988672308 cites W2070979828 @default.
• W1988672308 cites W2072251608 @default.
• W1988672308 cites W2076940193 @default.
• W1988672308 cites W2091665377 @default.
• W1988672308 cites W2095059453 @default.
• W1988672308 cites W2333555861 @default.
• W1988672308 cites W2952641675 @default.
• W1988672308 cites W2962941170 @default.
• W1988672308 hasPublicationYear "2012" @default.
• W1988672308 type Work @default.
• W1988672308 sameAs 1988672308 @default.
• W1988672308 citedByCount "0" @default.
• W1988672308 crossrefType "posted-content" @default.
• W1988672308 hasAuthorship W1988672308A5017685495 @default.
• W1988672308 hasConcept C114614502 @default.
• W1988672308 hasConcept C118615104 @default.
• W1988672308 hasConcept C121332964 @default.
• W1988672308 hasConcept C12657307 @default.
• W1988672308 hasConcept C136170076 @default.
• W1988672308 hasConcept C141071460 @default.
• W1988672308 hasConcept C162838799 @default.
• W1988672308 hasConcept C199360897 @default.
• W1988672308 hasConcept C202444582 @default.
• W1988672308 hasConcept C203492994 @default.
• W1988672308 hasConcept C20725272 @default.
• W1988672308 hasConcept C2780990831 @default.
• W1988672308 hasConcept C2781311116 @default.
• W1988672308 hasConcept C33923547 @default.
• W1988672308 hasConcept C41008148 @default.
• W1988672308 hasConcept C46875033 @default.
• W1988672308 hasConcept C62520636 @default.
• W1988672308 hasConcept C71924100 @default.
• W1988672308 hasConcept C76572486 @default.
• W1988672308 hasConcept C77461463 @default.
• W1988672308 hasConcept C9555016 @default.
• W1988672308 hasConcept C9652623 @default.
• W1988672308 hasConcept C97137487 @default.
• W1988672308 hasConcept C98486379 @default.
• W1988672308 hasConceptScore W1988672308C114614502 @default.
• W1988672308 hasConceptScore W1988672308C118615104 @default.
• W1988672308 hasConceptScore W1988672308C121332964 @default.
• W1988672308 hasConceptScore W1988672308C12657307 @default.
• W1988672308 hasConceptScore W1988672308C136170076 @default.
• W1988672308 hasConceptScore W1988672308C141071460 @default.
• W1988672308 hasConceptScore W1988672308C162838799 @default.
• W1988672308 hasConceptScore W1988672308C199360897 @default.
• W1988672308 hasConceptScore W1988672308C202444582 @default.
• W1988672308 hasConceptScore W1988672308C203492994 @default.
• W1988672308 hasConceptScore W1988672308C20725272 @default.
• W1988672308 hasConceptScore W1988672308C2780990831 @default.
• W1988672308 hasConceptScore W1988672308C2781311116 @default.
• W1988672308 hasConceptScore W1988672308C33923547 @default.
• W1988672308 hasConceptScore W1988672308C41008148 @default.
• W1988672308 hasConceptScore W1988672308C46875033 @default.
• W1988672308 hasConceptScore W1988672308C62520636 @default.
• W1988672308 hasConceptScore W1988672308C71924100 @default.
• W1988672308 hasConceptScore W1988672308C76572486 @default.
• W1988672308 hasConceptScore W1988672308C77461463 @default.
• W1988672308 hasConceptScore W1988672308C9555016 @default.
• W1988672308 hasConceptScore W1988672308C9652623 @default.
• W1988672308 hasConceptScore W1988672308C97137487 @default.
• W1988672308 hasConceptScore W1988672308C98486379 @default.
• W1988672308 hasLocation W19886723081 @default.
• W1988672308 hasOpenAccess W1988672308 @default.
• W1988672308 hasPrimaryLocation W19886723081 @default.
• W1988672308 hasRelatedWork W1966356968 @default.
• W1988672308 hasRelatedWork W1972078097 @default.
• W1988672308 hasRelatedWork W1983735493 @default.
• W1988672308 hasRelatedWork W2007114628 @default.
• W1988672308 hasRelatedWork W2043055027 @default.
• W1988672308 hasRelatedWork W2051223427 @default.
• W1988672308 hasRelatedWork W2059660033 @default.
• W1988672308 hasRelatedWork W2107501402 @default.
• W1988672308 hasRelatedWork W2121192631 @default.
• W1988672308 hasRelatedWork W2166418814 @default.
• W1988672308 hasRelatedWork W2558716033 @default.
• W1988672308 hasRelatedWork W2560366722 @default.
• W1988672308 hasRelatedWork W2902756806 @default.
• W1988672308 hasRelatedWork W2949217035 @default.
• W1988672308 hasRelatedWork W2963071451 @default.

• next