Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals which are intersections of prime ideal powers. We can characterize the Cohen-Macaulayness of the second symbolic power or of all symbolic powers of a Stanley-Reisner ideal in terms of the simplicial complex. These characterizations show that the simplicial complex must be very compact if some symbolic power is Cohen-Macaulay. In particular, all symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid complex. We also prove that the Cohen-Macaulayness can pass from a symbolic power to another symbolic powers in different ways.Comment: The published version of this paper contains a gap in the proofs of Theorem 2.5 and Theorem 3.5. This version corrects the proofs with almost the same arguments. Moreover, we have to modify the definition of tight complexes in Theorem 2.5. These changes don't affect other things in the published version. A corrigendum has been sent to the journa

Book review: Symbolic power, politics and intellectuals: the political sociology of Pierre Bourdieu

"Symbolic Power, Politics and Intellectuals: The Political Sociology of Pierre Bourdieu." David L. Swartz. University of Chicago Press. May 2013. --- Power is the central organizing principle of all social life, from culture and education to stratification and taste. And there is no more prominent name in the analysis of power than that of Pierre Bourdieu. In Symbolic Power, Politics, and Intellectuals, David L. Swartz delves into Bourdieu’s work to show how central – but often overlooked – power and politics are to an understanding of sociology. This book can be regarded as a superb piece of analysis, as well as a great read, and one which successfully sheds light on a neglected aspect of Bourdieu’s work, concludes Luke McDonagh

Comparison of symbolic and ordinary powers of ideals

In this paper we generalize the theorem of Ein-Lazarsfeld-Smith (concerning the behavior of symbolic powers of prime ideals in regular rings finitely generated over a field of characteristic 0) to arbitrary regular rings containing a field. The basic theorem states that in such rings, if P is a prime ideal of height c, then for all n, the symbolic (cn)th power of P is contained in the nth power of P. Results are also given in the non-regular case: one must correct by a power of the Jacobian ideal in rings where the Jacobian ideal is defined

The Symbolic Narrative of the Body in Murniasih’s Paintings : an Hermeneutical Study

This article is a study on I.G.K Murniasih’s paintings on the perspective of hermeneutics. It focuses on the aspects of symbolic-narrative, i.e. the narrative elements which optimized the potentials of symbols. The study has successfully defined the symbolic narrative in visual works, specifically in Murniasih’s tings. Symbolic narrative in visual works is in line with suggestive narrative in literary works. The symbolic narrative is formed by symbolic elements that are related each other to build a structure and a narrative pattern. In Murniasih’s works the narrative elements are supported by and originated from Murni’s biographical body; the experiencing body. In other words, Murniasih’s paintings are those which tell about the body related to he bio graphical experience. In addition, it is thematically found that the symbolic narrative is around the relationship between men and women in various episodes; the relationship of harmony, domination, ideology, power, and rebellion

Media psychology, symbolic power and social justice in Aotearoa

Psychologists reside in a world saturated by media. We work in professional contexts where guidelines for practice foreground ethical obligations to address issues of social justice. This paper addresses both these contextual dimensions of psychological research and practice. We explore the social significance of increased media production by Maori in challenging the tendency in mainstream media to marginalize Maori concerns while promoting Pakeha perspectives. The analysis focuses on the recent 'Inside Out documentary - Hikoi', which was initiated by two young Maori women as a challenge to media framing of Maori protests as 'unjustified' and 'disruptive' acts. We illustrate how this documentary furthers public dialogue regarding the foreshore and seabed controversy by promoting an alternative depiction of a Maori protest, which emphasize the history of grievances and social unity. The implications of such representations for psychologists working to address issues of social justice and to challenge abuses of symbolic power are discussed