In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...

In a ring with an involution, we first present some necessary and sufficient conditions for the existence of $m$-weak group inverse expression. As application, prove that regular element $a$ is $(m+1)$-weak invertible if only $a^2a^{-}$ invertible, where $a^{-}$ inner $a$. The relevant results weak core inverses pseudocore are given. addition, new characterizations inverses, also investigate ma...

Short-range entangled topological phases of matter are closely connected to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological Phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented ...

Given a bounded operator A on a Banach space X with Drazin inverse A and index r, we study the class of group invertible bounded operators B such that / + A (B — A) is invertible and 1Z(B) f]N(A) = {0}. We show that they can be written with respect to the decomposition X = lZ(A) 0 Af(A) as a matrix operator, B = ( _ _ __i _ ), where B\ and B\ + B\9#?1 a r e invertible. ^ if21 t>2\tf\ i*\2 Sever...

Abstract We use the Blanchfield form to obtain a lower bound on equivariant slice genus of strongly invertible knot. For our main application, let be one knot with nontrivial Alexander polynomial. show that an connected sum is at least . also formulate algebraic concordance group, and kernel forgetful map classical group infinite rank.

We study the algebraic and arithmetic structure of monoids invertible ideals (more precisely, $r$-invertible $r$-ideals for certain ideal systems $r$) Krull weakly Mori domains. also investigate all nonzero polynomial rings with at least two indeterminates over noetherian Among others, we show that they are not transfer but share several arithmetical phenomena having infinite class group prime ...

We give two explicit sets of generators the group invertible regular functions over Q on modular curve Y 1 (N).