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Algebra Commons

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Articles 1 - 4 of 4

Full-Text Articles in Algebra

About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger Oct 2018

About A Non-Standard Interpolation Problem, Daniel Alpay, Alain Yger

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein algebra, using the Lagrange interpolation polynomial, plays a key role in the arguments.


Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, Peter Jipsen, Fei Liang, M. Andrew Moshier, Apostolos Tzimoulis Aug 2018

Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, Peter Jipsen, Fei Liang, M. Andrew Moshier, Apostolos Tzimoulis

Mathematics, Physics, and Computer Science Faculty Articles and Research

"We define partially-ordered multi-type algebras and use them as algebraic semantics for multi-type display calculi that have recently been developed for several logics, including dynamic epistemic logic [7], linear logic[10], lattice logic [11], bilattice logic [9] and semi-De Morgan logic [8]."


Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon May 2018

Nonassociative Right Hoops, Peter Jipsen, Michael Kinyon

Mathematics, Physics, and Computer Science Faculty Articles and Research

The class of nonassociative right hoops, or narhoops for short, is defined as a subclass of right-residuated magmas, and is shown to be a variety. These algebras generalize both right quasigroups and right hoops, and we characterize the subvarieties in which the operation x ^^ y = (x/y)y is associative and/or commutative. Narhoops with a left unit are proved to be integral if and only if ^ is commutative, and their congruences are determined by the equivalence class of the left unit. We also prove that the four identities defining narhoops are independent.


On Lattices Of Z-Ideals Of Function Rings, Themba Dube, Oghenetega Ighedo Mar 2018

On Lattices Of Z-Ideals Of Function Rings, Themba Dube, Oghenetega Ighedo

Mathematics, Physics, and Computer Science Faculty Articles and Research

An ideal I of a ring A is a z-ideal if whenever a, bA belong to the same maximal ideals of A and aI, then bI as well. On the other hand, an ideal J of A is a d-ideal if Ann2(a) ⊆ J for every aJ. It is known that the lattices Z(L) and D(L) of the ring 𝓡L of continuous real-valued functions on a frame L, consisting of z-ideals and d-ideals of 𝓡 …