Idempotent States and the Inner Linearity Property

The Aluffi Algebra and Linearity Condition

The Aluffi algebra is an algebraic version of characteristic cycles in intersection theory which is an intermediate graded algebra between the symmetric algebra (naive blowup) and the Rees algebra (blowup). Let  R be a commutative Noetherian ring and J ⊂I  ideals of R. We say that J ⊂I  satisfy linearity condition if the Aluffi algebra of I/J is isomorphic with the symmetric algebra. In this pa...

City-States and the Inner Sea

Fully idempotent and coidempotent modules

In this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von Neumann's regular rings. Furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators

A unary operator f is idempotent if the equation f(x) = f(f(x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator if a = a a. This paper presents a rule format for Structural Operational Semantics that guarantees that a unary operator be idempotent modulo bisimilarity. The proposed rule format relies on a companion one ensuring that certain te...

The Reeh–Schlieder Property for Ground States

Recently it has been shown that the Reeh–Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.