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Z -pencils.

McDonald, Judith J., Olesky, D.Dale, Schneider, Hans, Tsatsomeros, Michael J., van den Driessche, P. (1998)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Zero-divisors of content algebras

Peyman Nasehpour (2010)

Archivum Mathematicum

In this article, we prove that in content extentions minimal primes extend to minimal primes and discuss zero-divisors of a content algebra over a ring who has Property (A) or whose set of zero-divisors is a finite union of prime ideals. We also examine the preservation of diameter of zero-divisor graph under content extensions.

Zero-one laws for graphs with edge probabilities decaying with distance. Part II

Saharon Shelah (2005)

Fundamenta Mathematicae

Let Gₙ be the random graph on [n] = 1,...,n with the probability of i,j being an edge decaying as a power of the distance, specifically the probability being p | i - j | = 1 / | i - j | α , where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a “finite compactness”. Lastly, as a consequence, we prove that the zero-one law (for first order logic)...

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