Sentence examples for minimal hereditary subset from inspiring English sources

In view of minimality of W it contains W. It implies that for any two minimal hereditary subset (W_1, W_2) either (W_1=W_2) or (W_1cap W_2=emptyset.) The collection (W_1,ldots, W_k) of all distinct minimal nonempty hereditary subsets of V is called the frame of (Gamma.) Every vertex of (Gamma ) has a descendant in (mathop {cup }nolimits _{ige 1}^k W_i).

Remark that each component (S_i) intersects just one minimal hereditary subset (W_i).

Indeed, if the Leavitt path algebra (L(Gamma )) is prime then the frame consists of one minimal hereditary subset (W_1).

Indeed, the only minimal hereditary subset of V is ({w}.) There are infinitely many special paths with all vertices lying in (V{setminus }{w}={v}.) Let (Gamma = ) Open image in new window The graph (Gamma = V,E)) does not have proper hereditary subsets.

By the proof of Lemma 13 arbitrary specializations of non-sink minimal hereditary subsets (gamma _i:W_irightarrow E(W_i, W_i)) can be extended to a specialization (gamma :V rightarrow E) with the property (1).

Let W be a minimal nonempty hereditary subset of V. Then for any two vertices (w_1,W_2in W) the vertex (w_2) is a descendant of (w_1).

Let W be a minimal nonempty hereditary subset of V. Then the ideal I(W) is generated (as an ideal) by all idempotents (e_w, w in W).

The only minimal nonempty hereditary subset is ({w}.) If the cycle c is special then there are infinitely many special path (c^i, ige 1,) having all vertices outside of (mathop {cup }nolimits _{ige 1}^k W_i={w}.) If the edge e is special then there is only one such special path e.

Indeed, the set of all descendants of (w_1) is a hereditary subset of V.

Let W be a nonempty hereditary subset of V. Let (W^bot subset V) consist of those vertices which do not have descendants in W. Clearly, (W^bot ) is a hereditary subset of V.

Any subset of U is a hereditary subset of C N 0. We note also that, since saturation applies only to regular vertices, any subset of U is saturated as well.