Bitz, Ginoux, Jacobson, Nizkorodov, and Yang Receive 2013 Atmospheric Sciences Ascent Awards: Citation for Mark Z. Jacobson

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Alec Jacobson Teaching Statement

My passion for teaching began early. Throughout high school and college, I tutored English to African immigrants. Later, while student teaching remedial and gifted-and-talented mathematics at a New York City public middle school, I realized the diversity of how students learn. Some students thrive off interactive lectures, while others do not fully digest a lecture until working out examples at...

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$n$-Array Jacobson graphs

We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.

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Distributive Lattices of Jacobson Rings

We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.

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The Jacobson Density Theorem and Applications

1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...

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ژورنال

عنوان ژورنال: Eos, Transactions American Geophysical Union

سال: 2014

ISSN: 0096-3941

DOI: 10.1002/2014eo290011